Question

complete the following truth table. use t for true and f for false. in this table, p and q are statements.

Explanation:

Step1: Define negation rule

$\sim q$ is opposite of $q$: if $q=T$, $\sim q=F$; if $q=F$, $\sim q=T$.

Step2: Define disjunction rule

$q \lor p$ is T if at least one of $q,p$ is T; else F.

Step3: Fill $\sim q$ column

For row1 ($q=T$): $\sim q=F$; row2 ($q=F$): $\sim q=T$; row3 ($q=T$): $\sim q=F$; row4 ($q=F$): $\sim q=T$.

Step4: Fill $q \lor p$ column

Row1 ($q=T,p=T$): $T\lor T=T$; row2 ($q=F,p=T$): $F\lor T=T$; row3 ($q=T,p=F$): $T\lor F=T$; row4 ($q=F,p=F$): $F\lor F=F$.

Answer:

$p$	$q$	$\sim q$	$q \lor p$
T	F	T	T
F	T	F	T
F	F	T	F