The dual of the statement - p - - q - p - q - r- is-

The correct option is D ∼ p ∨ [∼ q ∨ (p∧ q) ∨∼ r] The dual of the statement ∼ p ∧ [∼ q ∧ (p ∨ q) ∧∼ #160;r] is ≡ #160; ∼ p ∨ [∼ q ∨ (p∧ q) ∨ ...

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Logical Connectives

The dual of t...

Question

The dual of the statement $\sim p \land [\sim q \land (p \lor q) \land \sim r]$ is:

\sim p \lor [\sim q \lor (p \lor q) \lor \sim r]

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p \lor [q \lor (\sim p \land \sim q) \lor r]

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\sim p \lor [\sim q \lor (p \land q) \lor \sim r]

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\sim p \lor [\sim q \land (p \land q) \land \sim r]

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Solution

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The dual of statement $p \lor (q \land r) \equiv (p \lor q) \land (p \lor r)$ is

Factorise: $(p^{2} + q^{2} - r^{2})^{2} - 4 p^{2} q^{2}$

The contrapositive of $(\sim p \land q) \to (q \land \sim r)$ is

(p - q)^{3} + (q - r)^{3} + (r - p)^{3}

p \land [\sim q \lor (p \land q) \lor \sim r]

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