Chapter B.1, Problem 12E

Solution

The completed truth table.

It has been determined that the completed truth table is as follows:

$p$	$q$	$\sim p$	$\sim q$	$\sim p\vee q$
T	T	F	F	T
T	F	F	T	F
F	T	T	F	T
F	F	T	T	T

Given:

The incomplete truth table:

$p$	$q$	$\sim p$	$\sim q$	$\sim p\vee q$
T	T
T	F
F	T
F	F

Concept used:

The truth value of an expression can be determined based on the truth value of the variables in the expression.

Calculation:

Completing the given truth table as follows:

$p$	$q$	$\sim p$	$\sim q$	$\sim p\vee q$
T	T	F	F	T
T	F	F	T	F
F	T	T	F	T
F	F	T	T	T

Conclusion:

It has been determined that the completed truth table is as follows:

$p$	$q$	$\sim p$	$\sim q$	$\sim p\vee q$
T	T	F	F	T
T	F	F	T	F
F	T	T	F	T
F	F	T	T	T