Question

Disprove the statement: Let a, b, and c be sets. If a ∪ b = a ∪ c, then b = c?

1) True
2) False

Answer 1

The statement is false. A counterexample can be provided to disprove the statement.

Step-by-step explanation:

The statement is false. To disprove the statement, we can provide a counterexample where b is not equal to c. Let's say a = {1, 2}, b = {2, 3}, and c = {1, 3}. In this case, a ∪ b = {1, 2, 3} = a ∪ c but b ≠ c. Therefore, we have shown that the statement is false.