Let p, q, r be three logical statements. Consider the compound statements S_1:(( p) q) (( p) r) and S_2: p arrow(q r) Then, which of the following is NOT true?

Correct answer: C. If S_2 is false, then S_1 is true Given statement S_1:( p q) ( p r) p (q r)S_2: p arrow(q r) p (q r) arrow By conditional law S_1 S_2

BITSAT 2024Paper 1

Exam: BITSAT
Year: 2024
Paper: Paper 1
Subject: Mathematics
Chapter: Mathematical Reasoning

BITSAT 2024 · Paper 1 · Mathematics · Mathematical Reasoning

Let p, q, r be three logical statements. Consider the compound...

Let

p, q, r

be three logical statements. Consider the compound statements

S_1:((\sim p) \vee q) \vee((\sim p) \vee r)

and

S_2: p \rightarrow(q \vee r)

Then, which of the following is NOT true?

Options

AIf $S_2$ is true, then $S_1$ is true
BIf $S_2$ is false, then $S_1$ is false
CIf $S_2$ is false, then $S_1$ is true
DIf $S_1$ is false, then $S_2$ is false

Correct answer

C. If $S_2$ is false, then $S_1$ is true

Step-by-step solution

Given statement

S_1:(\sim p \vee q) \vee(\sim p \vee r)\equiv \sim p \vee(q \vee r)S_2: p \rightarrow(q \vee r)\equiv \sim p \vee(q \vee r) \rightarrow

By conditional law

S_1 \equiv S_2

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