Which one of the following Boolean expressions is a tautology?

  • Option 1)

    (p\wedge q)\vee (p\wedge \sim q)

  • Option 2)

    (p\vee q)\vee (p\vee \sim q)

  • Option 3)

    (p\vee q)\wedge (p\vee \sim q)

  • Option 4)

    (p\vee q)\wedge (\sim p\vee \sim q)

 

Answers (1)

1.) (p\wedge q)\vee (p\wedge \sim q) \equivp\wedge (q\vee \sim q)\equiv p\wedge t\equiv p (p\vee q)\wedge \sim (p\wedge q) 

2.) (p\vee q)\wedge ( p\vee \sim q)\equivp\vee (q\vee \sim q)\equiv p\vee t\equiv t

3.) (p\vee q)\wedge (p\vee \sim q)\equivp\vee (q\vee \sim q)\equiv p\vee f\equiv p

not tautology (take both p & q as T )

4.) (p\vee q)\wedge ( \sim p\vee \sim q)\equiv(p\vee q)\wedge \sim (p\wedge q)\rightarrow

not tautology (take both p & q as T )

So, option (2) is correct.


Option 1)

(p\wedge q)\vee (p\wedge \sim q)

Option 2)

(p\vee q)\vee (p\vee \sim q)

Option 3)

(p\vee q)\wedge (p\vee \sim q)

Option 4)

(p\vee q)\wedge (\sim p\vee \sim q)

Most Viewed Questions

Preparation Products

Knockout JEE Main (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Expert Mentorship, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
Buy Now
Knockout JEE Main (Nine Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Expert Mentorship, - Study Improvement Plan.

₹ 13999/- ₹ 12499/-
Buy Now
Knockout JEE Main (One Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Expert Mentorship, - Study Improvement Plan.

₹ 2999/- ₹ 1999/-
Buy Now
Knockout JEE Main (Twelve Months Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Expert Mentorship, - Study Improvement Plan.

₹ 19999/- ₹ 14499/-
Buy Now
Knockout JEE Main (Eight Months Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Expert Mentorship, - Study Improvement Plan.

₹ 15999/- ₹ 12499/-
Buy Now
Boost your Preparation for JEE Main 2021 with Personlized Coaching
 
Exams
Articles
Questions