Given the sets U={0,1,2,3,4,5,6,7,8,9}, A={3,6,9}, and B={2,4,6,8}. Evaluate (A’ ∪ B) ∩ B’.A) {0,1,5,8}B) {0,1,3,5,7,9}C) {0,1,2,4,5,6,7,8}D) {0,1,5,7}

To evaluate the expression (A' ∪ B) ∩ B', we need to follow these steps:

Step 1: Find the complement of set A, denoted as A'. The complement of A contains all the elements in the universal set U that are not in A. In this case, A' = {0,1,2,4,5,7,8}.

Step 2: Find the union of A' and B, denoted as (A' ∪ B). The union of two sets contains all the elements that are in either set. In this case, (A' ∪ B) = {0,1,2,4,5,6,7,8}.

Step 3: Find the complement of set B, denoted as B'. The complement of B contains all the elements in the universal set U that are not in B. In this case, B' = {0,1,3,5,7,9}.

Step 4: Find the intersection of (A' ∪ B) and B', denoted as (A' ∪ B) ∩ B'. The intersection of two sets contains all the elements that are common to both sets. In this case, (A' ∪ B) ∩ B' = {0,1,5,7}.

Therefore, the correct answer is D) {0,1,5,7}.

To evaluate the expression (A' ∪ B) ∩ B', we need to follow these steps:

Step 1: Find the complement of set A, denoted as A'. The complement of A contains all the elements in the universal set U that are not in A. In this case, A' = {0,1,2,4,5,7,8}.

Step 2: Find the union of A' and B, denoted as (A' ∪ B). The union of two sets contains all the elements that are in either set. In this case, (A' ∪ B) = {0,1,2,4,5,6,7,8}.

Step 3: Find the complement of set B, denoted as B'. The complement of B contains all the elements in the universal set U that are not in B. In this case, B' = {0,1,3,5,7,9}.

Step 4: Find the intersection of (A' ∪ B) and B', denoted as (A' ∪ B) ∩ B'. The intersection of two sets contains all the elements that are common to both sets. In this case, (A' ∪ B) ∩ B' = {0,1,5,7}.

Therefore, the correct answer is D) {0,1,5,7}.