Question

A Venn Diagram shows Sets A and B.

A Venn Diagram is titled Universal Set with the rectangle labeled U and the left circle labeled A and the right circle labeled B. The two circles overlap, and the overlap includes the elements 2 and 6. The A circle outside the overlap contains the elements 4 and 9 and 10, and the B circle outside the overlap contains the elements 3 and 5 and 7 and 8. The element 1 lies outside both circles.

Part A: Determine the elements in A ∩ B. Justify the answer using the Venn Diagram. (2 points)

Part B: Determine the elements in ~(A ∩ B). Justify the answer using the Venn Diagram. (3 points)

Part C: Determine the elements in A ∪ B. Justify the answer using the Venn Diagram. (2 points)

Part D: Determine the elements in A ∪ ~B. Justify the answer using the Venn Diagram. (3 points)

Answer 1

@toga

Answer 2

For Part A, the elements in A ∩ B are 2 and 6. This is because the intersection of sets A and B is the overlapping region of the two circles, which contains only 2 and 6.

For Part B, ~(A ∩ B) represents the complement of the intersection of sets A and B, which includes all the elements outside of the overlapping region of the two circles. So, ~(A ∩ B) includes 1, 3, 4, 5, 7, 8, 9, and 10.

For Part C, the elements in A ∪ B represent the union of sets A and B, which includes all the elements in both sets. So, A ∪ B includes 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.

For Part D, A ∪ ~B represents the union of set A and the complement of set B, which includes all the elements in set A as well as any elements that are not in set B. So, A ∪ ~B includes 1, 2, 4, 6, 9, and 10.