Question

Which three statements would produce the truth value F when p is true and q is false?

A. p -> q
B. ~p/\~q
C. p->~q
D. q\/~p
C. p/\~q
please help

Answer 1

B. If $p$ is true, then $\sim p$ (NOT $p$) is false; If $q$ is false, then $\sim q$ is true. Then $\sim p\land\sim q$ must be false, because both arguments are not true.

Answer 2

Answer with Step-by-step explanation:

p is true then ~p is false.

q is false then ~q is true.

A. p -> q

if p is true and q is false then this gives false truth value.

Hence, here truth value is F

B. ~p/\~q

if any one of them is false then it gives false truth value.

Hence, here truth value is F(since,~p is false)

C. p->~q

true statement implies a true statement hence, truth value will be true

Hence, here truth value is T(p true implies ~q true)

D. q\/~p

if any one of them is true then compound statement is true.

Hence, here truth value is F(since, ~p and q both are false)

E. p/\~q

if both true then compound statement is also true.

Hence, here truth value is T(since p and ~q both are true)