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Which of the following is not always tru...

Which of the following is not always true ?

A

`~ [ p vee (~q) ] equiv ~ p ^^ q`

B

`[( p vee q) vee (~q) ] ` is a tautology

C

`~( p rarr q) equiv (~p) ^^ `q

D

`~ [ p ^^ ( ~p) ] ` is a tautology

Text Solution

Verified by Experts

The correct Answer is:
C
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MCGROW HILL PUBLICATION-MATHEMATICAL REASONING -EXERCISE (CONCEPT-BASED (SINGLE CORRECT ANSWER TYPE QUESTIONS ))
  1. Which of the following is not a proposition ?

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  2. Which of the following is a statement?

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  3. Which of the following is not statement?

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  4. Suppose p and q are two statements and p vee (~q) is false, then trut...

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  5. Let p and q be the statements: p: It is cold. q: She needs a hot ...

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  6. Let p and q stand for the statements: p: Monica is old . q: She ...

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  7. If p to (~ p vvq) is false, the truth values of p and q are , respecti...

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  8. ~ p ^^ q is logically equivalent to

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  9. The negation of p ^^ (q to ~ r) is

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  10. Identify the false statement

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  11. If S(p,q,r)=(~p)vv(~(q ^^ r)) is a compound statement, then S(~p,~q,~r...

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  12. Which of the following statements is false

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  13. Which of the following statement is dual of p ^^ ( q vee r ) equiv ...

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  14. The statement (p rarr q ) rarr p is equivalent to

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  15. If p and q have truth value 'F', then the truth values of (~ p vv q) h...

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  16. Which of the following is a tautology ?

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  17. The proposition (p to ~p) ^^ (~p to p) is a

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  18. Which of the following is not always true ?

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  19. The converse of the contrapositive of the conditional p to ~ q is

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  20. Suppose t denotes the tautology and c denotes the contradiction. Let p...

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