Question

complete the following truth table. use t for true and f for false.
you may add more columns, but those added columns will not be graded.
$p$ $q$ $p\land \sim q$
t t
t f
f t
f f
not graded

Explanation:

Step1: Define negation of $q$

$\sim q$ is opposite of $q$:

• If $q=T$, $\sim q=F$
• If $q=F$, $\sim q=T$

Step2: Compute conjunction $p \land \sim q$

$p \land \sim q$ is T only if both $p$ and $\sim q$ are T:

• Row1: $T \land F = F$
• Row2: $T \land T = T$
• Row3: $F \land F = F$
• Row4: $F \land T = F$

Answer:

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