If p, q ~and& r are 3 statements, then the truth value of ((~ p ∨ q) ∧ ~ r) ⇒ p is

Correct answer: A. True if truth values of p, q, r are T, F, T respectively cases p & q & r & p & r & p ∨ q & ( p ∨ q) ∧ r & ( p ∨ q) ∧ r ⇒ p T & F & T & F & F & F & F & T T & F & F & F & T & F & F & T T & T & T & F & F & T & F & T cases

NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Mathematics
Chapter: Mathematical Reasoning

NTA Abhyas 2020 · Mathematics · Mathematical Reasoning

If p, q ~and& r are 3 statements, then the truth value of ((~ p ∨...

p, q

~and&

r

are

3

statements, then the truth value of \left(\left(~ p ∨ q\right) ∧ ~ r\right) ⇒ p$ is

Options

ATrue if truth values of $p, q, r$ are $T, F, T$ respectively
BFalse if truth values of $p, q, r$ are $T, F, T$ respectively
CFalse if truth values of $p, q, r$ are $T, F, F$ respectively
DFalse if truth values of $p, q, r$ are $T, T, T$ respectively

Correct answer

A. True if truth values of $p, q, r$ are $T, F, T$ respectively

Step-by-step solution

\begin{cases}p & q & r & p & r & p ∨ q & \left( p ∨ q\right) ∧ r & \left( p ∨ q\right) ∧ r ⇒ p \\ T & F & T & F & F & F & F & T \\ T & F & F & F & T & F & F & T \\ T & T & T & F & F & T & F & T\end{cases}

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