The negation of the Boolean expression \sim s\vee (\sim r\wedge s) 

is equivalent to :

  • Option 1)

    \sim s\wedge\sim r

  • Option 2)

    r

  • Option 3)

    s\vee r

  • Option 4)

    s\wedge r

 

Answers (1)

negation of the Boolean expression \sim s\vee (\sim r\wedge s) = \sim(\sim s)\wedge\sim (\sim r\wedge s)

Applying De morgans law,

\sim(A\vee B)=\sim A \: \wedge \sim B

= s\wedge (\sim(\sim r)\vee (\sim s))

=(s\wedge r)\vee(s\wedge \sim s)

Using double negation law and distributive law 

A\wedge (B\vee C)=(A\wedge B)\vee(A\wedge C)

=> (S\wedge r)\vee F

Contradiction (A\wedge \sim A)= F

=> (S\wedge r)

So, option (4) is correct.


Option 1)

\sim s\wedge\sim r

Option 2)

r

Option 3)

s\vee r

Option 4)

s\wedge r

Preparation Products

Knockout JEE Main April 2021 (One Month)

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 14000/- ₹ 6999/-
Buy Now
Knockout JEE Main April 2021

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 22999/- ₹ 14999/-
Buy Now
Test Series JEE Main April 2021

Take chapter-wise, subject-wise and Complete syllabus mock tests and get in depth analysis of your test..

₹ 6999/- ₹ 4999/-
Buy Now
Knockout JEE Main April 2022

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 34999/- ₹ 24999/-
Buy Now
JEE Main Rank Booster 2021

This course will help student to be better prepared and study in the right direction for JEE Main..

₹ 13999/- ₹ 9999/-
Buy Now
Boost your Preparation for JEE Main 2021 with Personlized Coaching
 
Exams
Articles
Questions