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  • I have a doubt, kindly clarify. Which one of the following Boolean expressions is a tautology?

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)

Posted by

Vakul

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