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Let the Universal set be {0,1,2,3,...}. Let A = {6, 10} and B = {4}. Find (A ⋂ B')AB'A'B

Question

Let the Universal set be {0,1,2,3,...}. Let A = {6, 10} and B = {4}. Find (AB)ABAB (A \cap B') A B' A' B

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Solution

Sure, let's break this down step by step.

  1. First, we need to understand the notation. "⋂" stands for intersection, which means the common elements between two sets. "B'" stands for the complement of B, which includes all elements in the universal set that are not in B.

  2. The universal set is {0,1,2,3,...}. Set A = {6, 10} and set B = {4}.

  3. The complement of B (B') would be all numbers except 4, since 4 is the only element in B. So, B' = {0,1,2,3,5,6,7,8,9,10,...}.

  4. Now, we find the intersection of A and B'. The intersection (A ⋂ B') would be the elements that are common to both A and B'. In this case, A ⋂ B' = {6, 10}.

  5. Now, let's find A'B'. A' is the complement of A, which includes all elements in the universal set that are not in A. So, A' = {0,1,2,3,4,5,7,8,9,...}. The intersection of A' and B' (A'B') would be the elements that are common to both A' and B'. In this case, A'B' = {0,1,2,3,5,7,8,9,...}.

  6. Finally, we need to find (A ⋂ B')AB'A'B. This notation is not standard and seems to be missing some operators. If you meant

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