Answer to Question #123575 in Discrete Mathematics for NOOR

Question

If p→q is false can you find the truth value of ~ (p ∧ q) →q? Explain your answer.

Answer 1

According to the definition of implication

$$p \rightarrow q$$

is false when p is true and q is false. Hence

$$p \land q$$

is false (a conjunction of false and true).

$$\neg (p \land q)$$

is true. Therefore using the definition of implication

$$\neg (p \land q) \rightarrow q$$

is false (true implication false).

Answer. the resulting value is false.