If the truth value of the Boolean expression ( ( p ∨ q ) ∧ ( q → r ) ∧ ( ~ r ) ) → ( p ∧ q ) is false, then the truth values of the statements p, q, r respectively can be:

Correct answer: B. TFF cases p & q & r & p ∨ q & q → r & ~ r & ( p ∨ q ) ∧ ( q → r ) ∧ ~ r & p ∧ q & ( ( p ∨ q ) ∧ ( q → r ) ∧ ~ r ) → p ∧ q T & T & T & T & T & F & F & T & T T & T & F & T & F & T & F & T & T T & F & T & T & T & F & F & F & T T & F & F & T & T & T & T & F & F F & T & T & T & T & F & F & F & T F & T & F & T & F & T & F & F & T F & F & T & F & T & F & F & F & T F & F & F & F & T & T & F & F & T cases

JEE Main 202126 AugustMorning Shift

Exam: JEE Main
Year: 2021
Date: 26 August
Shift: Morning Shift
Subject: Mathematics
Chapter: Mathematical Reasoning

JEE Main 2021 · 26 August · Morning Shift · Mathematics · Mathematical Reasoning

If the truth value of the Boolean expression ( ( p ∨ q ) ∧ ( q → r...

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

Options

A $FTF$
B $TFF$
C $TFT$
D $FFT$

Correct answer

B. $TFF$

Step-by-step solution

\begin{cases}p & q & r & p ∨ q & q \to r & ~ r & ( p ∨ q ) ∧ ( q \to r ) ∧ ~ r & p ∧ q & ( ( p ∨ q ) ∧ ( q \to r ) ∧ ~ r ) \to p ∧ q \\ \text{T} & T & T & T & T & F & F & T & T \\ T & T & F & T & F & T & F & T & T \\ T & F & T & T & T & F & F & F & T \\ T & F & F & T & T & T & T & F & F \\ F & T & T & T & T & F & F & F & T \\ F & T & F & T & F & T & F & F & T \\ F & F & T & F & T & F & F & F & T \\ F & F & F & F & T & T & F & F & T\end{cases}

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