If p is true and q is false, then which of the following statements is not true?

Question

If p is true and q is false, then which of the following statements is not true? (A) p∨ q (B) p⇒ q (C) p∧(-q) (D) p⇒ p

Tardigrade Admin · Accepted Answer

When p is true and q is false, then p∨ q is true, q⇒ p is true and p∧(∼ q)is true. ( ∵ both p and ∼ q are true) Here p⇒ q is not true as a true statement cannot imply a false statement.

Q. If p is true and q is false, then which of the following statements is not true?

$p \lor q$

$p \Rightarrow q$

$p \land (- q)$

$p \Rightarrow p$

When p is true and q is false, then $p \lor q$ is true, $q \Rightarrow p$ is true and $p \land (\sim q)$ is true.
( $∵$ both p and $\sim q$ are true)
Here $p \Rightarrow q$ is not true as a true statement cannot imply a false statement.