Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value (true or false) of this compound statement: A ↔ (C ⋁ D)

Question

Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value (true or false) of this compound statement:  A ↔ (C ⋁ D)

Quizplus · Accepted Answer

If A is true and D is false, then C ⋁ D is true only if C is true. For A ↔ (C ⋁ D) to be true, both sides must have the same truth value. Since A is true, (C ⋁ D) must also be true, which is possible if C is true. However, without knowing C's truth value, we cannot definitively determine the truth value of the compound statement, but assuming C is false, the statement is false.

Making the Assumption That a Is True, B Is True