Let U = {1,2,3,4,5,6,7,8,9}a) Given A = {2,4,6,8} (5)B = {2,3,5,7,}Verify (A ∪ B)’ = A’ ∩ B

To verify the given equation, we first need to understand what each symbol represents.

• "∪" is the union of two sets, which means all the elements that are in A, in B, or in both.
• "∩" is the intersection of two sets, which means only the elements that are common to both A and B.
• "’" is the complement of a set, which means all the elements in the universal set that are not in the given set.

Now, let's solve the equation step by step:

1. Calculate A ∪ B: The union of sets A and B includes all the unique elements from both sets. So, A ∪ B = {2,3,4,5,6,7,8}.

2. Calculate (A ∪ B)’: The complement of a set includes all the elements in the universal set that are not in the given set. So, (A ∪ B)’ = U - (A ∪ B) = {1,9}.

3. Calculate A’: The complement of A includes all the elements in the universal set that are not in A. So, A’ = U - A = {1,3,5,7,9}.

4. Calculate B: B is given as {2,3,5,7}.

5. Calculate A’ ∩ B: The intersection of sets A’ and B includes only the elements that are common to both sets. So, A’ ∩ B = {3,5,7}.

As we can see, (A ∪ B)’ = {1,9} and A’ ∩ B = {3,5,7} are not equal. Therefore, the given equation (A ∪ B)’ = A’ ∩ B is not correct.