Question

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

Explanation:

Step1: Define negation rule

$\sim p$ is opposite of $p$

Step2: Define conjunction rule

$p \land q$ is T only if $p,q$ are T

Step3: Fill $\sim p$ column

• $p=T$ → $\sim p=F$
• $p=F$ → $\sim p=T$

Step4: Fill $p \land q$ column

• $p=T,q=T$ → $p \land q=T$
• $p=T,q=F$ → $p \land q=F$
• $p=F,q=T$ → $p \land q=F$
• $p=F,q=F$ → $p \land q=F$

Answer:

$p$	$q$	$\sim p$	$p \land q$
T	F	F	F
F	T	T	F
F	F	T	F