Using truth tables, prove the following logical equivalence: $p \leftrightarrow q \equiv \sim [(p \lor q) \land \sim (p \land q)]$

| p | q | LHS: $p\leftrightarrow q$ | $p\lor q$ | $p\land q$ | $\sim(p\land q)$ | $(p\lor q)\land\sim(p\land q)$ | RHS: $\sim[\ldots]$ | |---|---|---|---|---|---|---|---| | T | T | T | T | T | F | F | T | | T | F | F | T | F | T | T | F | | F | T | F | T | F | T | T | F | | F | F | T | F | F | T | F | T | …

Using truth tables, prove the following logical equivalence: p rightarrow q ≡ sim [(p lor q) land sim (p land

Exercise 1.2 · Q55

p \leftrightarrow q \equiv \sim [(p \lor q) \land \sim (p \land q)]

Maharashtra MsbshseTextbookSubjectiveImportance★★★★★

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p	q	LHS: $p\leftrightarrow q$	$p\lor q$	$p\land q$	$\sim(p\land q)$	$(p\lor q)\land\sim(p\land q)$	RHS: $\sim[\ldots]$
T	T	T	T	T	F	F	T
T	F	F	T	F	T	T	F
F	T	F	T	F	T	T	F
F	F	T	F	F	T	F	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 2025Set ANNUAL2 marks

p\leftrightarrow q

›Reveal solution

Build the truth table for both statement patterns for every combination of $p,q$ and compare the final columns.

$p$	$q$	$\sim p$	$\sim q$	$p\leftrightarrow q$	$p\wedge q$	$\sim p\wedge\sim q$	$(p\wedge q)\vee(\sim p\wedge\sim q)$
T	T	F	F	T	T	F	T
T	F	F	T	F	F	F	F
F	T	T	F	F	F	F	F
F	F	T	T	T	F	T	T

The column for $p\leftrightarrow q$ is $[T, F, F, T]$ and the column for $(p\wedge q)\vee(\sim p\wedge\sim q)$ is also $[T, F, F, T]$ .

…

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CBSE 2022Set ANNUAL2 marks
$(p \wedge q) \vee \sim q \equiv p \vee \sim q$
›Reveal solutionSolution

Construct the truth table for both sides and compare all rows.

$p$ $q$ $p\wedge q$ $\sim q$ $(p\wedge q)\vee\sim q$ $p\vee\sim q$
T T T F T T
T F F T T T
F T F F F F
F F F T T T
…

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$p$	$q$	$p\wedge q$	$\sim q$	$(p\wedge q)\vee\sim q$	$p\vee\sim q$
T	T	T	F	T	T
T	F	F	T	T	T
F	T	F	F	F	F
F	F	F	T	T	T
…

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Q.Using truth tables, prove the following logical equivalence: $p \leftrightarrow q \equiv \sim [(p \lor q) \land \sim (p \land q)]$

Concept understanding — Logical Equivalence

Q.Using truth tables, prove the following logical equivalence: p↔q≡∼[(p∨q)∧∼(p∧q)]p \leftrightarrow q \equiv \sim [(p \lor q) \land \sim (p \land q)]p↔q≡∼[(p∨q)∧∼(p∧q)]

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Q.Using truth tables, prove the following logical equivalence: $p \leftrightarrow q \equiv \sim [(p \lor q) \land \sim (p \land q)]$

Unlock everything free for 14 days