Question

Let A = {a, b, c, d, e), B = {a, c, e, g), and C = (b, e, f, g). Then verify the following identities:

1. A ∩ B = {a, c, e}
2. A ∩ C = {b, e}
3. A ∪ B = {a, b, c, d, e, g}
4. B ∪ C = {a, c, e, f, g}

Answer 1

Verification of set identities is achieved by identifying common elements for intersections and combining elements for unions among sets A, B, and C.

Step-by-step explanation:

To verify the given set identities with the sets A = {a, b, c, d, e}, B = {a, c, e, g}, and C = {b, e, f, g}, we'll consider the definitions of set intersection (AND) and set union (OR)To verify the given identitiesA ∩ B refers to the intersection of sets A and B. The common elements between A and B are {ac, e}, which means A ∩ B = {a, c, e}A ∩ C refers to the intersection of sets A and C.

The common elements between A and C are {b, e}, so A ∩ C = {b, e}A ∪ B refers to the union of sets A and B. It includes all the elements in both sets, resulting in {a, b, c, d, e, g}, so A ∪ B = {a, b, c, d, e, g}.B ∪ C refers to the union of sets B and C. It includes all the elements in both sets, resulting in {a, c, e, f, g}, so B ∪ C = {a, c, e, f, g}.