First slide

Introduction to mathematical reasoning

Question

If $p \to (p \land ~ q)$ is false, then the truth values of p and q are respective

Easy

A

F, T
B

T,F
C

F, F
D

T,T

Solution

The statement $p \to (p \land (~ q))$ is false, if p is true and $p \land (~ q)$ is false and the statement $p \land (~ q)$ is false,
if $(~ q)$ is false as p is true, so q must be true.
So, the truth values of p and q are T, T respectively.
Hence, option (d) is correct.

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