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BITSAT 2023Paper 2
Exam
BITSAT
Year
2023
Paper
Paper 2
Subject
Mathematics
Chapter
Mathematical Reasoning

BITSAT 2023 · Paper 2 · Mathematics · Mathematical Reasoning

The negation of the Boolean expression (( q) p) (( p) q) is...

The negation of the Boolean expression ((∼q)∧p)⇒((∼p)∨q)((\sim q)\wedge p) \Rightarrow((\sim p) \vee q) is logically equivalent to

Options

  1. Ap⇒qp \Rightarrow q
  2. Bq⇒pq \Rightarrow p
  3. C∼(p⇒q)\sim(p \Rightarrow q)
  4. D∼(q⇒p)\sim(q \Rightarrow p)

Correct answer

C. ∼(p⇒q)\sim(p \Rightarrow q)

Step-by-step solution

Given boolen expression are∼p∨q≡p→q and  ∼q∧p≡∼(p→q) Negation of ∼(p→q)→(p→q) is ∼(p→q)∧(∼(p→q)) i.e., ∼(p→q)\begin{aligned} \\ & \sim p \vee q \equiv p \rightarrow q \text{\text{ and } } \sim q \wedge p \equiv \sim(p \rightarrow q) \\ \\ & \text{ Negation of } \sim(p \rightarrow q) \rightarrow(p \rightarrow q) \\ \\ & \text{ is } \sim(p \rightarrow q) \wedge(\sim(p \rightarrow q)) \text{ i.e., } \sim(p \rightarrow q) \\ \end{aligned}
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