Question

If $p$ is $T$ and $q$ is $F$, then which of the following have the truth value $T$?
$\left(i\right)p\vee q$
$\left(ii\right)\sim p\vee q$
$\left(iii\right)p\vee (\sim q)$
$\left(iv\right)p\wedge (\sim q)$

• A. $\left(i\right),\left(ii\right),\left(iii\right)$
• B. $\left(i\right),\left(ii\right),\left(iv\right)$
• C. $\left(i\right),\left(iii\right),\left(iv\right)$
• D. $\left(ii\right),\left(iii\right),\left(iv\right)$

Answer 1

Answer: (C)

$\left(i\right),\left(iii\right),\left(iv\right)$

$\left(i\right)p\vee q=T\vee F=T$
$\left(ii\right)\sim p\vee q=(\sim T)\vee F=F\vee F=F$
$\left(iii\right)p\vee (\sim q)=T\vee (\sim F)=T\vee T=T$
$\left(iv\right)p\wedge (\sim q)=T\wedge (\sim F)=T\wedge T=T$

Hence option 'C' is correct