Question

If $(p\wedge \sim q)\wedge (p\wedge r)\to \sim p\vee q$ is false, then the truth values of $p,q$ and $r$ are, repectively :

• A. $F,T,F$
• B. $T,F,T$
• C. $T,T,T$
• D. $F,F,F$

Answer 1

The correct option is B $T,F,T$

$(p\wedge \sim q)\wedge (p\wedge r)\to \sim p\vee q$ is false when $(p\wedge \sim q)\wedge (p\wedge r)$ is true and $\sim p\vee q$ is false

$\sim p\vee q$ is false when $p$ is true and $q$ is false
Now, $(p\wedge \sim q)\wedge (p\wedge r)$ will be true if $r$ is true

Hence, truth values of $p,q,r$ are $T,F,T$ respectively.