First slide

Introduction to mathematical reasoning

Question

If the compound statement $p \to (~ p \lor q)$ is false, then the truth value of p and q are respectively

Moderate

A

T,T
B

T,F
C

F,T
D

F,F

Solution

We know that, $p \to q$ is false only when p is true and q is false.
So, $p \to (~ p \lor q)$ is false only when p is true and $(~ p \lor q)$ is false.
But $(~ p \lor q)$ is false if q is false because $~ p$ is false.
Hence , $p \to (~ p \lor q)$ is false when truth value of p and q
are T and F respectively.

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