💡First, I need to determine the number of nests based on the information provided.I know that there are 6 birds and that there are 3 more birds than nests. This means the number of nests is 3 less than the number of birds.To find the number of nests, I subtract 3 from the total number of birds.So, 6 birds minus 3 equals 3 nests.Therefore, there are 3 nests.

💡Okay, so I'm trying to figure out this game between Uncle Fyodor and the cat Matroskin. They have 100N sandwiches, each with sausage and cheese. Uncle Fyodor eats sandwiches from either end, one at a time, and he does this 100 times in a row each turn. Matroskin, on his turn, can remove the sausage from one sandwich or do nothing. The goal for Uncle Fyodor is to have the last sandwich he eats still have sausage. I need to determine if Uncle Fyodor can always win, no matter what Matroskin does, for any natural number N.First, let me break down the rules:1. **Number of Sandwiches**: There are 100N sandwiches. So, depending on N, this could be a large number, but it's always a multiple of 100.2. **Uncle Fyodor's Move**: He eats one sandwich from either end of the line of sandwiches. He does this 100 times in a row each turn. So, each turn, he reduces the number of sandwiches by 100.3. **Matroskin's Move**: He can remove the sausage from one sandwich or do nothing. So, each turn, he can potentially make one sandwich inedible in terms of sausage, but he can also choose not to do anything.4. **Turn Order**: Uncle Fyodor goes first, then Matroskin, and they alternate until all sandwiches are eaten.5. **Winning Condition**: Uncle Fyodor wins if the last sandwich he eats still has sausage. So, he needs to ensure that when he's eating the last sandwich, it hasn't been deprived of sausage by Matroskin.Now, I need to see if Uncle Fyodor can always win, regardless of Matroskin's actions. Let me think about the strategies each player might use.Uncle Fyodor's strategy should be about controlling the flow of sandwiches he eats, ensuring that the last one is still intact. Since he eats from either end, he can choose which side to eat from, which might help him manage the order in which sandwiches are consumed.Matroskin, on the other hand, wants to remove sausages in such a way that the last sandwich Uncle Fyodor eats has no sausage. Since Matroskin can only remove one sausage per turn, he has to be strategic about which sandwich to target.Let me consider the number of turns each player will have. Since there are 100N sandwiches and Uncle Fyodor eats 100 per turn, he will have N turns. Matroskin, going second, will have N-1 turns because he starts after Uncle Fyodor. So, Matroskin can remove at most N-1 sausages.Wait, so if there are 100N sandwiches, and Matroskin can remove N-1 sausages, that leaves 100N - (N-1) = 99N +1 sandwiches with sausages. But Uncle Fyodor is eating all of them, so he will eat all 100N sandwiches, but only N-1 of them might be without sausage. So, the last sandwich he eats could still have sausage.But that seems too simplistic. Maybe I'm missing something.Wait, no. Because Matroskin can choose which specific sandwiches to remove the sausage from. So, he can target the last sandwiches that Uncle Fyodor is going to eat. If Matroskin can predict or influence which sandwiches will be last, he can remove their sausages.But how can Matroskin influence which sandwiches are last? Since Uncle Fyodor is eating from either end, the order in which sandwiches are eaten depends on Uncle Fyodor's choices. If Uncle Fyodor can control the order, he can decide which sandwiches are eaten first and which are last.But Matroskin can only remove one sausage per turn. So, if Matroskin removes a sausage from a sandwich, he can potentially make that sandwich inedible for Uncle Fyodor in terms of sausage. But Uncle Fyodor still has to eat all sandwiches, so he will eat the one without sausage, but he only cares about the last one.So, if Matroskin can remove the sausage from the last sandwich, he can make Uncle Fyodor lose. But how can he ensure that?Wait, the problem is that Uncle Fyodor is eating 100 sandwiches per turn, so the last sandwich he eats is the 100Nth sandwich. But Matroskin can only remove one sausage per turn, so he can only target one sandwich per turn.But over N turns, Matroskin can remove N-1 sausages. So, he can target N-1 sandwiches. If he can target the last N-1 sandwiches, he can remove their sausages, making the last sandwich Uncle Fyodor eats the only one without sausage. But wait, that would mean the last sandwich still has sausage, because Matroskin only removed N-1.Wait, no. If there are 100N sandwiches, and Matroskin removes N-1 sausages, then there are 100N - (N-1) = 99N +1 sandwiches with sausages. So, the last sandwich could still have sausage.But Matroskin can choose which sandwiches to remove. If he removes the sausages from the last N-1 sandwiches, then the last sandwich would still have sausage. So, Uncle Fyodor would win.Alternatively, if Matroskin removes sausages from the first N-1 sandwiches, then the last sandwich would still have sausage. So, in either case, the last sandwich would have sausage.Wait, but Matroskin can only remove one sausage per turn, so he can't remove N-1 sausages in one turn. He has to do it over N-1 turns.But Uncle Fyodor is eating 100 sandwiches per turn, so the number of sandwiches decreases by 100 each turn. So, the last turn, Uncle Fyodor will eat the last 100 sandwiches. But Matroskin can only have removed N-1 sausages by then.So, in the last 100 sandwiches, at most N-1 have had their sausages removed. So, if N-1 is less than 100, which it is for N <= 101, then there are still sausages left in the last 100 sandwiches. So, Uncle Fyodor can choose to eat a sandwich with sausage as his last one.But wait, for larger N, say N=100, then Matroskin can remove 99 sausages, so in the last 100 sandwiches, 99 could be without sausage. So, only one sandwich has sausage. Uncle Fyodor can choose that one as his last.But what if N is larger, like N=101? Then Matroskin can remove 100 sausages, so in the last 100 sandwiches, all could be without sausage. Then, Uncle Fyodor would have to eat a sandwich without sausage as his last one, making him lose.Wait, but N=101 would mean 100*101=10100 sandwiches. Matroskin can remove 100 sausages, so he can target 100 specific sandwiches. If he removes sausages from the last 100 sandwiches, then Uncle Fyodor's last 100 would all be without sausage. So, Uncle Fyodor would lose.But wait, the problem says "for any natural number N". So, if N=101, Uncle Fyodor cannot guarantee a win, because Matroskin can remove sausages from the last 100 sandwiches, making them all without sausage.But the problem is asking if Uncle Fyodor can always win regardless of Matroskin's moves for any natural number N. So, if for some N, like N=101, Uncle Fyodor cannot guarantee a win, then the answer would be no.But wait, maybe I'm missing something. Maybe Uncle Fyodor can control the order in which he eats the sandwiches, so that he can avoid the sandwiches that Matroskin has targeted.But Matroskin can only remove one sausage per turn, so he can't remove all sausages from the last 100 sandwiches unless N is large enough.Wait, let's think about it more carefully.Suppose N=1. Then there are 100 sandwiches. Uncle Fyodor eats all 100 in his first turn. Matroskin doesn't get to move because after Uncle Fyodor's first turn, all sandwiches are eaten. So, Uncle Fyodor wins because the last sandwich he eats has sausage.For N=2, there are 200 sandwiches. Uncle Fyodor eats 100 in his first turn, leaving 100. Then Matroskin removes one sausage, leaving 99 with sausage. Then Uncle Fyodor eats the remaining 100, but one of them is without sausage. So, the last sandwich he eats could be without sausage, but he might choose to eat the one with sausage last. Wait, can he choose the order?Wait, the problem says Uncle Fyodor eats one sandwich from one of the edges each action. So, he can choose which end to eat from, but he can't choose specific sandwiches beyond that. So, if Matroskin removes a sausage from a sandwich in the middle, Uncle Fyodor might have to eat it eventually.Wait, but if Matroskin removes a sausage from a sandwich, it's still a sandwich, just without sausage. Uncle Fyodor has to eat it, but he only cares about the last one having sausage.So, in the case of N=2, after Uncle Fyodor's first turn, there are 100 sandwiches left. Matroskin removes one sausage, so 99 have sausage. Then Uncle Fyodor eats the remaining 100, but one of them is without sausage. So, the last sandwich he eats could be without sausage, but he might have eaten the one without sausage earlier.Wait, but since he eats from the edges, if Matroskin removes a sausage from a sandwich in the middle, Uncle Fyodor might not reach it until later. But if Matroskin removes a sausage from a sandwich near the end, Uncle Fyodor could eat it earlier.Hmm, this is getting complicated. Maybe I need a different approach.Let me think about the total number of sausages Matroskin can remove. He can remove at most N-1 sausages because he has N-1 turns. So, in the entire game, he can make N-1 sandwiches without sausage.Uncle Fyodor eats all 100N sandwiches, so he will eat N-1 sandwiches without sausage and 100N - (N-1) with sausage. So, the last sandwich he eats could be one of the 100N - (N-1) with sausage, or one of the N-1 without.But Matroskin can choose which sandwiches to remove the sausages from. If he can target the last N-1 sandwiches, then the last N-1 sandwiches would be without sausage, and the 100N - (N-1) would be with. But Uncle Fyodor is eating from the edges, so the last sandwiches he eats are the ones in the middle if he alternates sides.Wait, no. If he eats from one end, say the left, then the last sandwich would be the rightmost one. If he alternates, it's more complicated.Wait, maybe Uncle Fyodor can control the order by choosing which side to eat from each time. So, he can decide to eat from the left or the right each time, potentially controlling which sandwiches are eaten when.If that's the case, he can ensure that the last sandwich he eats is one that hasn't had its sausage removed. Because Matroskin can only remove N-1 sausages, and there are 100N sandwiches, so there are still 100N - (N-1) sandwiches with sausage. So, as long as Uncle Fyodor can choose the order, he can make sure that the last sandwich is one of the ones with sausage.But wait, Matroskin can remove sausages from specific sandwiches. If Matroskin removes sausages from the last N-1 sandwiches, then the last N-1 sandwiches would be without sausage, and the first 100N - (N-1) would be with. But Uncle Fyodor is eating from the edges, so he would eat the first N-1 sandwiches first, leaving the last N-1 without sausage. But he would have to eat all 100N, so he would have to eat the last N-1 without sausage, but he only cares about the last one.Wait, no. If Matroskin removes sausages from the last N-1 sandwiches, then when Uncle Fyodor is eating from the left, he would eat the first 100N - (N-1) sandwiches with sausage, and then the last N-1 without. So, the last sandwich he eats would be without sausage, making him lose.But if Uncle Fyodor can choose to eat from the right instead, he could eat the last N-1 sandwiches first, which are without sausage, and then the remaining would be with. But he has to eat all 100N, so he would have to eat the last N-1 without sausage, but he only cares about the last one.Wait, I'm getting confused. Let me try to formalize this.Let’s denote the sandwiches as S1, S2, ..., S_{100N}.Matroskin can remove sausages from up to N-1 sandwiches. Let's say he removes sausages from the last N-1 sandwiches: S_{100N - N + 2}, ..., S_{100N}.Then, when Uncle Fyodor eats from the left, he would eat S1 to S_{100N - N +1} with sausage, and then S_{100N - N +2} to S_{100N} without. So, the last sandwich he eats would be S_{100N}, which is without sausage.But if Uncle Fyodor instead eats from the right, he would eat S_{100N} first, which is without sausage, and then proceed to eat the rest. But he has to eat all 100N, so the last sandwich he eats would be S1, which still has sausage.Wait, so if Uncle Fyodor chooses to eat from the right, he can make sure that the last sandwich he eats is S1, which hasn't had its sausage removed. Because Matroskin only removed sausages from the last N-1 sandwiches.So, in this case, Uncle Fyodor can choose to eat from the right, making the last sandwich S1, which still has sausage.But wait, Matroskin could have removed sausages from the first N-1 sandwiches instead. Then, if Uncle Fyodor eats from the left, the last sandwich would be S_{100N}, which still has sausage. If he eats from the right, the last sandwich would be S1, which is without sausage.But Uncle Fyodor can choose which side to eat from. So, he can choose the side that leaves the last sandwich with sausage.Wait, but Matroskin can choose which sandwiches to remove sausages from. If he removes sausages from both ends, then Uncle Fyodor might not be able to avoid it.But Matroskin can only remove one sausage per turn, so over N-1 turns, he can remove N-1 sausages. He can't remove sausages from both ends effectively because he can only target one sandwich per turn.Wait, but if Matroskin removes sausages from the middle sandwiches, then Uncle Fyodor might have to eat them eventually, but he can choose the order.This is getting too vague. Maybe I need a mathematical approach.Let’s consider the total number of sausages Matroskin can remove: N-1.Uncle Fyodor needs to ensure that the last sandwich he eats is among the 100N - (N-1) sandwiches that still have sausage.If Uncle Fyodor can control the order, he can choose to leave the last sandwich as one that hasn't been targeted by Matroskin.But how?Wait, if Uncle Fyodor eats from one end, say the left, then the order is fixed: he eats S1, S2, ..., S_{100N}. If Matroskin removes sausages from the last N-1 sandwiches, then the last N-1 would be without sausage, and the last sandwich would be without.But if Uncle Fyodor instead eats from the right, he eats S_{100N}, S_{100N-1}, ..., S1. If Matroskin removed sausages from the last N-1 (which are now the first N-1 when eating from the right), then the last sandwich would be S1, which still has sausage.So, Uncle Fyodor can choose the direction to eat from such that the last sandwich is one that Matroskin didn't target.But Matroskin can choose which sandwiches to remove. If he removes sausages from both ends, but he can only remove one per turn, so he can't cover both ends effectively.Wait, but if Matroskin removes sausages from the middle, then Uncle Fyodor might have to eat them eventually, but he can choose the order.Wait, perhaps the key is that Matroskin can only remove N-1 sausages, so there are 100N - (N-1) sandwiches with sausage. Uncle Fyodor can choose the order to eat such that the last sandwich is among the ones with sausage.But how can he ensure that? Because Matroskin can choose which specific sandwiches to remove.Wait, maybe it's about the parity or something else.Alternatively, think about it as a game where Uncle Fyodor can always mirror Matroskin's moves or something.Wait, perhaps the answer is yes, Uncle Fyodor can always win, because he can control the order of eating, and since Matroskin can only remove N-1 sausages, Uncle Fyodor can always leave the last sandwich as one that hasn't been targeted.But earlier, I thought that if Matroskin removes sausages from the last N-1 sandwiches, then if Uncle Fyodor eats from the left, the last sandwich would be without sausage. But if he eats from the right, the last sandwich would be S1, which still has sausage.So, Uncle Fyodor can choose the direction to eat from, ensuring that the last sandwich is one that Matroskin didn't target.Therefore, regardless of which sandwiches Matroskin removes, Uncle Fyodor can choose the direction to eat from such that the last sandwich is still with sausage.Wait, but what if Matroskin removes sausages from both ends? For example, he removes one from the first sandwich and one from the last sandwich in different turns. Then, if Uncle Fyodor eats from the left, the last sandwich would be without sausage. If he eats from the right, the last sandwich would be without sausage as well. So, in that case, Uncle Fyodor cannot win.But wait, Matroskin can only remove one sausage per turn, so he can't remove both S1 and S_{100N} unless N >=2.Wait, for N=2, Matroskin has 1 turn to remove one sausage. So, he can remove either S1 or S_{100N}, but not both. So, Uncle Fyodor can choose the direction to eat from, avoiding the one without sausage.But for larger N, say N=3, Matroskin has 2 turns, so he can remove two sausages, maybe from S1 and S_{100N}. Then, if Uncle Fyodor eats from the left, the last sandwich would be without sausage. If he eats from the right, the last sandwich would be without sausage as well. So, he cannot win.Wait, but for N=3, there are 300 sandwiches. Matroskin can remove 2 sausages. If he removes from S1 and S300, then regardless of which direction Uncle Fyodor eats from, the last sandwich would be without sausage.But wait, Uncle Fyodor eats 100 sandwiches per turn. So, in the first turn, he eats 100, leaving 200. Matroskin removes one sausage, say from S1. Then, Uncle Fyodor eats another 100, leaving 100. Matroskin removes another sausage, say from S300. Then, Uncle Fyodor eats the last 100, which includes S300. So, the last sandwich he eats is S300, which is without sausage.But if Uncle Fyodor chooses to eat from the right in his last turn, he would eat S300 first, then proceed to eat the rest. But he has to eat all 100, so the last one would be S201, which still has sausage.Wait, no. If he eats from the right in his last turn, he would eat S300, S299, ..., S201. So, the last sandwich he eats is S201, which still has sausage. So, he wins.Wait, but Matroskin removed sausage from S300, so S300 is without sausage. But Uncle Fyodor can choose to eat S300 first, making it the first of his last 100, and then the last one would be S201, which still has sausage.So, even if Matroskin removes sausages from both ends, Uncle Fyodor can choose the direction to eat from in his last turn, ensuring that the last sandwich is still with sausage.Wait, but Matroskin can only remove N-1 sausages. So, for N=3, he can remove 2 sausages. If he removes them from S1 and S300, then Uncle Fyodor can choose to eat from the right in his last turn, making the last sandwich S201, which still has sausage.Similarly, for larger N, Matroskin can remove N-1 sausages, but Uncle Fyodor can choose the direction to eat from in his last turn, leaving the last sandwich as one that hasn't been targeted.Therefore, regardless of how Matroskin removes the sausages, Uncle Fyodor can always choose the direction to eat from in his last turn, ensuring that the last sandwich he eats is still with sausage.Wait, but what if Matroskin removes sausages from the middle sandwiches? Then, Uncle Fyodor would have to eat them eventually, but he can choose the order.Wait, but the last sandwich is determined by the direction he eats from. So, if he eats from the left, the last sandwich is S_{100N}. If he eats from the right, it's S1. If he alternates, it's more complicated, but he can choose the direction in his last turn.So, if Matroskin removes sausages from the middle, Uncle Fyodor can still choose the direction to eat from in his last turn, making the last sandwich either S1 or S_{100N}, which Matroskin hasn't targeted because he only removed N-1 sausages.Wait, but Matroskin could have removed sausages from both S1 and S_{100N}, but he can only do that if N-1 >=2, which is for N>=3.But as we saw earlier, even if Matroskin removes sausages from both ends, Uncle Fyodor can choose the direction to eat from in his last turn, making the last sandwich the one that wasn't targeted.Wait, but if Matroskin removes sausages from both ends, then Uncle Fyodor has to eat one of them as his last sandwich, but he can choose which one.Wait, no. If Matroskin removes sausages from both S1 and S_{100N}, then Uncle Fyodor can choose to eat from the left, making the last sandwich S_{100N}, which is without sausage. Or he can eat from the right, making the last sandwich S1, which is without sausage. So, in that case, he cannot win.But wait, Matroskin can only remove N-1 sausages. So, for N=3, he can remove 2 sausages, say from S1 and S300. Then, Uncle Fyodor has to eat all 300. If he eats from the left, the last sandwich is S300, without sausage. If he eats from the right, the last sandwich is S1, without sausage. So, he cannot win.But earlier, I thought that Uncle Fyodor can choose the direction in his last turn, but actually, the direction is determined by his previous choices. He can't arbitrarily choose the direction in the last turn because he has to eat 100 sandwiches each turn.Wait, no. Uncle Fyodor eats 100 sandwiches per turn, but he can choose which end to eat from each time. So, in his last turn, he can choose to eat from the left or the right, whichever leaves the last sandwich with sausage.But if Matroskin has removed sausages from both ends, then regardless of which direction Uncle Fyodor chooses, the last sandwich would be without sausage.Wait, but Matroskin can only remove N-1 sausages. So, for N=3, he can remove 2 sausages. If he removes them from S1 and S300, then Uncle Fyodor has to eat both in his last turn, but he can choose the order.Wait, no. Uncle Fyodor eats 100 sandwiches per turn. So, in his last turn, he has to eat the remaining 100 sandwiches, which include S1 and S300. If he eats from the left, he eats S1 first, then S2, ..., up to S100. If he eats from the right, he eats S300 first, then S299, ..., up to S201.But the last sandwich he eats in his last turn would be either S100 or S201, depending on the direction. If Matroskin removed sausages from S1 and S300, then S100 and S201 still have sausages. So, the last sandwich he eats would still have sausage.Wait, that's a good point. Because Matroskin can only remove N-1 sausages, which is 2 for N=3, he can only target 2 sandwiches. So, in the last 100 sandwiches, only 2 are without sausage. So, the last sandwich Uncle Fyodor eats is one of the 100, and only 2 are without sausage. So, he can choose to eat the one with sausage last.Wait, but how? Because he eats 100 sandwiches in a row, he can't choose the order within that turn. He can only choose the direction to eat from.So, if he eats from the left, he eats S1 to S100 in his first turn, then S101 to S200 in his second, and S201 to S300 in his third. Matroskin removes sausages from S1 and S300. So, in his third turn, Uncle Fyodor eats S201 to S300. If he eats from the left, he eats S201 first, then S202, ..., up to S300. The last sandwich he eats is S300, which is without sausage. If he eats from the right, he eats S300 first, then S299, ..., up to S201. The last sandwich he eats is S201, which still has sausage.Ah, so by choosing to eat from the right in his last turn, he can make sure that the last sandwich he eats is S201, which still has sausage.Therefore, even if Matroskin removes sausages from both ends, Uncle Fyodor can choose the direction in his last turn to eat from, ensuring that the last sandwich is still with sausage.This seems to generalize. For any N, Matroskin can remove N-1 sausages, but Uncle Fyodor can choose the direction in his last turn to eat from, leaving the last sandwich as one that hasn't been targeted.Therefore, Uncle Fyodor can always win, regardless of Matroskin's moves, for any natural number N.

💡Okay, so I have this binary number, "11110," and I need to convert it to its decimal representation. Hmm, I remember that binary numbers are base-2, which means each digit represents a power of 2. But I'm a bit rusty on the exact steps, so let me think this through carefully.First, I should recall how binary numbers work. Each digit in a binary number corresponds to a power of 2, starting from the rightmost digit, which is 2^0. As we move to the left, the exponent increases by 1. So, for the number "11110," the rightmost digit is the 0th position, then moving left, we have positions 1, 2, 3, and 4.Let me write down the number with its positions:Position: 4 3 2 1 0Binary: 1 1 1 1 0Wait, that doesn't seem right. The rightmost digit should be position 0, so if the number is "11110," the positions should be:Position: 4 3 2 1 0Binary: 1 1 1 1 0Yes, that's correct. So, the rightmost digit is 0, which is in position 0, and the leftmost digit is 1, which is in position 4.Now, to convert this to decimal, I need to calculate the value of each digit multiplied by 2 raised to the power of its position, and then sum all those values.Let's break it down:Starting from the right:- The 0th position: 0 * 2^0 = 0 * 1 = 0- The 1st position: 1 * 2^1 = 1 * 2 = 2- The 2nd position: 1 * 2^2 = 1 * 4 = 4- The 3rd position: 1 * 2^3 = 1 * 8 = 8- The 4th position: 1 * 2^4 = 1 * 16 = 16Now, I'll add all these values together:0 + 2 + 4 + 8 + 16Let me do the addition step by step to avoid mistakes:- 0 + 2 = 2- 2 + 4 = 6- 6 + 8 = 14- 14 + 16 = 30So, the total is 30. Therefore, the binary number "11110" should convert to the decimal number 30.Wait a second, let me double-check to make sure I didn't make any errors in my calculations. Sometimes, when dealing with exponents, it's easy to miscount or miscalculate.Starting again:- Position 0: 0 * 1 = 0- Position 1: 1 * 2 = 2- Position 2: 1 * 4 = 4- Position 3: 1 * 8 = 8- Position 4: 1 * 16 = 16Adding them up:0 + 2 = 22 + 4 = 66 + 8 = 1414 + 16 = 30Yes, that still gives me 30. Okay, I think that's correct.Just to be thorough, maybe I can use another method to verify. I've heard of the doubling method for converting binary to decimal. Let me try that.Starting from the leftmost digit:- Take the first digit: 1- Double it and add the next digit: (1 * 2) + 1 = 2 + 1 = 3- Double the result and add the next digit: (3 * 2) + 1 = 6 + 1 = 7- Double the result and add the next digit: (7 * 2) + 1 = 14 + 1 = 15- Double the result and add the next digit: (15 * 2) + 0 = 30 + 0 = 30Okay, using the doubling method also gives me 30. That matches my previous result, so I'm more confident now that 30 is the correct decimal equivalent of the binary number "11110."I think I've got it right. The binary number "11110" converts to 30 in decimal.

💡First, calculate the total number of student volunteers by multiplying the number of math classes by the number of students from each class.Next, subtract the number of student volunteers from the total number of volunteers needed to determine how many more volunteers are required.Finally, subtract the number of additional volunteers still needed from the total number of volunteers required to find out how many teachers have already volunteered.

💡First, identify the elements in set ( A ) and set ( B ).Set ( A ) contains the elements ( {1, 2, 3, 5} ).Set ( B ) contains the elements ( {2, 3, 6} ).The union of sets ( A ) and ( B ), denoted ( A cup B ), includes all distinct elements that are present in either set ( A ) or set ( B ).Combine the elements from both sets, ensuring there are no duplicates.The combined elements are ( 1, 2, 3, 5, 6 ).Therefore, the union of sets ( A ) and ( B ) is ( {1, 2, 3, 5, 6} ).

💡First, I need to determine how many boys are absent. There are 70 boys in total, and 1/7 of them are absent. So, I calculate 1/7 of 70, which equals 10 boys.Next, I calculate the number of girls absent. There are 50 girls in total, and 1/5 of them are absent. Therefore, 1/5 of 50 equals 10 girls.Now, I add the number of absent boys and girls to find the total number of absent students: 10 boys + 10 girls = 20 students absent.Finally, to find the percentage of the total student population that is absent, I divide the number of absent students by the total number of students and multiply by 100. So, 20 divided by 120 equals 1/6, which is approximately 16.67%.Therefore, the percentage of the total student population that is absent is 16.67%.