Question

If the truth value of the Boolean expression $((p\vee q)\wedge (q\to r)\wedge (\sim r))\to (p\wedge q)$ is false, then the truth values of the statements $p,q,r$ respectively can be:

• A. T F T
• B. F F T
• C. T F F
• D. F T F

Answer 1

Answer: (C)

$p$	$q$	$r$	$\underset{a}{\underbrace{p\vee q}}$	$\underset{b}{\underbrace{q\to r}}$	$a\wedge b$	$\sim r$	$\underset{c}{\underbrace{a\wedge b\wedge (\sim r)}}$	$\underset{d}{\underbrace{p\wedge q}}$	$c\to d$
T	F	T	T	T	T	F	F	F	T
F	F	T	F	T	F	F	F	F	T
T	F	F	T	T	T	T	T	F	F
F	T	F	T	F	F	T	F	F	T