Negation of the Boolean statement p - q - r - p is equivalent to

P ∨ q ⇒(∼ r ∨ p) amp;≡∼(p ∨ q) ∨(∼ r ∨ p) amp;≡(∼ p ∧∼ q) ∨(p ∨∼ r) amp;≡[(∼ p ∨ p) ∧(∼ q ∨ p)] ∨∼ r amp;≡(∼ q ∨ p) ∨∼ r Its negation is ∼ p ∧ q ∧ r ...

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Standard XII

Mathematics

Fallacy

Negation of t...

Question

Negation of the Boolean statement $(p \lor q) \Rightarrow ((\sim r) \lor p)$ is equivalent to

(\sim p) \land (\sim q) \land r

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p \land (\sim q) \land r

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(\sim p) \land q \land r

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p \land q \land (\sim r)

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Solution

The correct option is C $(\sim p) \land q \land r$
$p \lor q \Rightarrow (\sim r \lor p)$
$\begin{matrix} \equiv\sim (p \lor q) \lor (\sim r \lor p) \equiv (\sim p \land \sim q) \lor (p \lor \sim r) \equiv [(\sim p \lor p) \land (\sim q \lor p)] \lor \sim r \equiv (\sim q \lor p) \lor \sim r \end{matrix}$
Its negation is $\sim p \land q \land r$ .

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Negation of the Boolean statement (p∨q)⇒((∼r)∨p) is equivalent to

The correct option is C (∼p)∧q∧rp∨q⇒(∼r∨p) ≡∼(p∨q)∨(∼r∨p)≡(∼p∧∼q)∨(p∨∼r)≡[(∼p∨p)∧(∼q∨p)]∨∼r≡(∼q∨p)∨∼r Its negation is ∼p∧q∧r.

Negation of the Boolean statement $(p \lor q) \Rightarrow ((\sim r) \lor p)$ is equivalent to