Question

If the truth value of the statement
(P∧(∼R))->((∼R)∧Q)
is F , then the truth value of which of the following is F?

• A. P∨Q->∼R
• B. R∨Q->∼P
• C. ∼(P∨Q)->∼R
• D. ∼(R∨Q)->∼P

Answer 1

Answer: (D)

∼(R∨Q)->∼P

Answer 2

The correct answer is(D): ∼(R∨Q)→∼P.

$\underbrace{P∧(∼R)X→}$ $\underbrace{((∼R)∧Q)Y }$ = False
x y

X → Y = False

X	Y	X→Y
F	F	T
T	T	T
F	T	T
T	F	F

P∧∼R = T and (∼R)∧Q = F
⇒ P = T
∼R = T ⇒ R = F
⇒ P = T, Q = F and R = F
T∧Q = F
⇒ Q = F
Now ∼(R∨Q)→∼P
∼(F∨F)→∼F
F→F = False