Construct the truth table for the following statement pattern: $[p \rightarrow (q \rightarrow r)] \leftrightarrow [(p \land q) \rightarrow r]$

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

Construct the truth table for the following statement pattern: [p arrow (q arrow r)] rightarrow [(p land q) ar

Exercise 1.2 · Q50

[p \rightarrow (q \rightarrow r)] \leftrightarrow [(p \land q) \rightarrow r]

Maharashtra MsbshseTextbookSubjectiveImportance★★★★★

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p	q	r	$q\rightarrow r$	$p\rightarrow(q\rightarrow r)$	$p\land q$	$(p\land q)\rightarrow r$	$\leftrightarrow$
T	T	T	T	T	T	T	T
T	T	F	F	F	T	F	T
T	F	T	T	T	F	T	T
T	F	F	T	T	F	T	T
F	T	T	T	T	F	T	T
F	T	F	F	T	F	T	T

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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: $[p \rightarrow (q \rightarrow r)] \leftrightarrow [(p \land q) \rightarrow r]$

Concept understanding — Statement Patterns and Truth Tables

Q.Construct the truth table for the following statement pattern: [p→(q→r)]↔[(p∧q)→r][p \rightarrow (q \rightarrow r)] \leftrightarrow [(p \land q) \rightarrow r][p→(q→r)]↔[(p∧q)→r]

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Q.Construct the truth table for the following statement pattern: $[p \rightarrow (q \rightarrow r)] \leftrightarrow [(p \land q) \rightarrow r]$

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