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.
$p$ $q$ $\sim p \lor \sim q$
t t
t f
f t
f f
not graded

Explanation:

Step1: Define negation values

For $p$: $\sim p = \text{F}$ when $p=\text{T}$, $\sim p = \text{T}$ when $p=\text{F}$; For $q$: $\sim q = \text{F}$ when $q=\text{T}$, $\sim q = \text{T}$ when $q=\text{F}$

Step2: Evaluate row 1 (p=T,q=T)

$\sim p = \text{F}$, $\sim q = \text{F}$. $\text{F} \lor \text{F} = \text{F}$

Step3: Evaluate row 2 (p=T,q=F)

$\sim p = \text{F}$, $\sim q = \text{T}$. $\text{F} \lor \text{T} = \text{T}$

Step4: Evaluate row 3 (p=F,q=T)

$\sim p = \text{T}$, $\sim q = \text{F}$. $\text{T} \lor \text{F} = \text{T}$

Step5: Evaluate row 4 (p=F,q=F)

$\sim p = \text{T}$, $\sim q = \text{T}$. $\text{T} \lor \text{T} = \text{T}$

Answer:

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