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BITSAT 2024
Exam
BITSAT
Year
2024
Subject
Mathematics
Chapter
Mathematical Reasoning

BITSAT 2024 · Mathematics · Mathematical Reasoning

The Boolean expression (p q) ( p q) is equivalent to

The Boolean expression ∼(p∨q)∨(∼p∧q)\sim(p \vee q) \vee(\sim p \wedge q) is equivalent to

Options

  1. App
  2. Bqq
  3. C∼q\sim q
  4. D∼p\sim p

Correct answer

D. ∼p\sim p

Step-by-step solution

 Given, ∼(p∨q)∨(∼p∧q)⇒(∼p∧∼q)∨(∼p∧q) (By De Morgan’s Law) ⇒∼p∧(∼q∨q) (Distributive Law) ⇒∼p∧t (By complement law, where t= tautology) ⇒∼p (Identity law) \begin{aligned} & \text{ Given, } \sim(p \vee q) \vee(\sim p \wedge q) \\ & \Rightarrow(\sim p \wedge \sim q) \vee(\sim p \wedge q) \text{ (By De Morgan's Law) } \\ & \Rightarrow \sim p \wedge(\sim q \vee q) \text{ (Distributive Law) } \\ & \Rightarrow \sim p \wedge t \text{ (By complement law, where } t=\text{ tautology) } \\ & \Rightarrow \sim p \text{ (Identity law) }\end{aligned}
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