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

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

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

Exercise 1.2 · Q61

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

Maharashtra MsbshseTextbookSubjectiveImportance★★★★★

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p	q	$p\leftrightarrow q$	LHS: $\sim(p\leftrightarrow q)$	$\sim q$	$\sim p$	$p\land\sim q$	$q\land\sim p$	RHS
T	T	T	F	F	F	F	F	F
T	F	F	T	T	F	T	F	T
F	T	F	T	F	T	F	T	T
F	F	T	F	T	T	F	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 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: $\sim (p \leftrightarrow q) \equiv (p \land \sim q) \lor (q \land \sim p)$

Concept understanding — Logical Equivalence

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

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

Unlock everything free for 14 days