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.
$p$ $q$ $\sim q \
ightarrow \sim p$
t t
t f
f t
f f

Explanation:

Step1: Define negations

For each row, calculate $\sim p$ and $\sim q$:

• Row1: $\sim p = F$, $\sim q = F$
• Row2: $\sim p = F$, $\sim q = T$
• Row3: $\sim p = T$, $\sim q = F$
• Row4: $\sim p = T$, $\sim q = T$

Step2: Evaluate implication rule

Recall $A
ightarrow B$ is F **only** when $A=T$ and $B=F$; else T.

• Row1: $F

ightarrow F = T$

• Row2: $T

ightarrow F = F$

• Row3: $F

ightarrow T = T$

• Row4: $T

ightarrow T = T$

Answer:

$p$

$q$

$\sim q

ightarrow \sim p$ |

T	T	T
T	F	F
F	T	T
F	F	T