Question

If statement $(p\to q)\to (q\to r)$ is false, then truth values of statements $p,q,r$ respectively, can be :

• A. $FTF$
• B. $TTT$
• C. $FFF$
• D. $FTT$

Answer 1

The correct option is A $FTF$

p	q	r	$p\to q$	$q\to r$	$(p\to q)\to (q\to r)$
T	T	T	T	T	T
T	T	F	T	F	F
T	F	T	F	T	T
T	F	F	F	T	T
F	T	T	T	T	T
F	T	F	T	F	F
F	F	T	T	T	T
F	F	F	T	T	T

$\therefore$ If p=T or p=F

q=T q=T

r=F r=F

Then the statement $(p\to q)\to (q\to r)$ is false.