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’b) Given A = {3,5,7,9,11} (5)B = {7,9,11,13}C = {15,17}Find A ∩ (B ∪ C)

Sure, let's solve these problems step by step.

a) We have A = {2,4,6,8} and B = {2,3,5,7}.

First, let's find A ∪ B, which is the union of sets A and B. This means we combine all the elements of A and B, but we don't repeat any elements. So, A ∪ B = {2,3,4,5,6,7,8}.

Next, let's find the complement of A ∪ B, which is (A ∪ B)'. This means we take all the elements in the universal set U that are not in A ∪ B. So, (A ∪ B)' = {1,9}.

Now, let's find the complements of A and B, which are A' and B'. A' = {1,3,5,7,9} and B' = {1,4,6,8,9}.

Finally, let's find the intersection of A' and B', which is A' ∩ B'. This means we take all the elements that are in both A' and B'. So, A' ∩ B' = {1,9}.

So, we have verified that (A ∪ B)' = A' ∩ B'.

b) We have A = {3,5,7,9,11}, B = {7,9,11,13}, and C = {15,17}.

First, let's find B ∪ C, which is the union of sets B and C. This means we combine all the elements of B and C, but we don't repeat any elements. So, B ∪ C = {7,9,11,13,15,17}.

Next, let's find A ∩ (B ∪ C), which is the intersection of set A and the union of sets B and C. This means we take all the elements that are in both A and (B ∪ C). So, A ∩ (B ∪ C) = {7,9,11}.