Construct the truth table for the following statement pattern: $(\sim p \rightarrow \sim q) \land (\sim q \rightarrow \sim p)$

| p | q | $\sim p$ | $\sim q$ | $\sim p\rightarrow\sim q$ | $\sim q\rightarrow\sim p$ | $(\sim p\rightarrow\sim q)\land(\sim q\rightarrow\sim p)$ | |---|---|---|---|---|---|---| | T | T | F | F | T | T | T | | T | F | F | T | T | F | F | …

Construct the truth table for the following statement pattern: (sim p arrow sim q) land (sim q arrow sim p)

Exercise 1.2 · Q48

(\sim p \rightarrow \sim q) \land (\sim q \rightarrow \sim p)

Maharashtra MsbshseTextbookSubjectiveImportance★★★★★

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p	q	$\sim p$	$\sim q$	$\sim p\rightarrow\sim q$	$\sim q\rightarrow\sim p$	$(\sim p\rightarrow\sim q)\land(\sim q\rightarrow\sim p)$
T	T	F	F	T	T	T
T	F	F	T	T	F	F

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Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

CBSE 2024Set ANNUAL2 marks
$[(p\rightarrow q)\wedge q]\rightarrow p$
›Reveal solutionSolution

Build the columns $p\to q$ , $(p\to q)\wedge q$ , then $\to p$ .

$p$ $q$ $p\to q$ $(p\to q)\wedge q$ $[(p\to q)\wedge q]\to p$
T T T T T
T F F F T

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CBSE 2023Set ANNUAL2 marksMCQ
$p \wedge q$
(a) T, T
(b) T, F
(c) F, T
(d) F, F
›Reveal solutionSolution

$p\to q$ is false only when $p=T,\ q=F$ ; check this satisfies $p\wedge q=F$ .

…

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$p$	$q$	$p\to q$	$(p\to q)\wedge q$	$[(p\to q)\wedge q]\to p$
T	T	T	T	T
T	F	F	F	T

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Q.Construct the truth table for the following statement pattern: $(\sim p \rightarrow \sim q) \land (\sim q \rightarrow \sim p)$

Concept understanding — Statement Patterns and Truth Tables

Q.Construct the truth table for the following statement pattern: (∼p→∼q)∧(∼q→∼p)(\sim p \rightarrow \sim q) \land (\sim q \rightarrow \sim p)(∼p→∼q)∧(∼q→∼p)

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Q.Construct the truth table for the following statement pattern: $(\sim p \rightarrow \sim q) \land (\sim q \rightarrow \sim p)$

Unlock everything free for 14 days