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JEE Main 20154 April
Exam
JEE Main
Year
2015
Date
4 April
Subject
Mathematics
Chapter
Mathematical Reasoning

JEE Main 2015 · 4 April · Mathematics · Mathematical Reasoning

The negation of ∽ s ∨ (∽ r ∧ s) is equivalent to

The negation of $∽ s ∨ \left(∽ r ∧ s\right) is equivalent to

Options

  1. As∧rs ∧ r
  2. Bs∧ rs ∧ ~ r
  3. Cs∧(r∧ s)s ∧ \left(r ∧ ~ s\right)
  4. Ds∨(r∨ s)s ∨ \left(r ∨ ~ s\right)

Correct answer

A. s∧rs ∧ r

Step-by-step solution

Given ∽(∽s∨(∽r∧s))=s∧[∽(∽r∧s)]∽ \left(∽ s ∨ \left(∽ r ∧ s\right)\right) = s ∧ \left[∽ \left(∽ r ∧ s\right)\right]

∵ (p∧q)=(∽p)∨(∽q)∵ ~ \left(p ∧ q\right) = \left(∽ p\right) ∨ \left(∽ q\right)

and ∽(p∨q)=(∽p)∧(∽q)∽ \left(p ∨ q\right) = \left(∽ p\right) ∧ \left(∽ q\right)

=s∧(r∨(∽s))= s ∧ \left(r ∨ \left(∽ s\right)\right)

=(s∧r)∨(s∧(∽s))= \left(s ∧ r\right) ∨ \left(s ∧ \left(∽ s\right)\right)

=(s∧r)∨F= \left(s ∧ r\right) ∨ F

=s∧r= s ∧ r
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