The Boolean expression p - q - q - p - q is equivalent toA- - p - qB- p - qC- P - qD- P - q

The correct option is C p ∨ qConsider, (p∧∼ q)∨ q∨ (∼ p∧ q) ≡ [(p∧∼ q )∨ q]∨ (∼ p ∧ q) . . .(Associtive Property) ≡ [(p∨ q)∧(∼ q ∨ q)]∨ (∼ p∧ q) . . .( ...

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Standard XII

Mathematics

Compound Statement

The Boolean e...

Question

The Boolean expression $(p \land \sim q) \lor q \lor (\sim p \land q)$ is equivalent to

\sim p \land q

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p \land q

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p \lor q

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p \lor \sim q

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Solution

The correct option is C $p \lor q$
Consider,
$(p \land \sim q) \lor q \lor (\sim p \land q) \equiv [(p \land \sim q) \lor q] \lor (\sim p \land q) . . . (A s s o c i t i v e P r o p e r t y) \equiv [(p \lor q) \land (\sim q \lor q)] \lor (\sim p \land q) . . . (D i s t r i b u t i v e P r o p e r t y) \equiv [(p \lor q) \land t] \lor (\sim p \land q) \equiv (p \lor q) \lor (\sim p \land q) . . . (∵ p \land t \equiv p) \equiv (p \lor q \lor \sim p) \land (p \lor q \lor q) \equiv (q \lor t) \land (p \lor q) \equiv t \land (p \lor q) \equiv p \lor q$

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The Boolean expression (p∧∼q)∨q∨(∼p∧q) is equivalent to

The Boolean expression $(p \land \sim q) \lor q \lor (\sim p \land q)$ is equivalent to