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Negation of the statement pto(q^^r) is...

Negation of the statement `pto(q^^r)` is

A

` ~ p to ~ ( q vv r)`

B

` ~ p to ~ ( q ^^ r)`

C

` ( q ^^ r) to p`

D

` p ^^ ( ~ q vv ~ r)`

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Verified by Experts

The correct Answer is:
D
we know that
` ~ ( p vv q) cong p ^^ ~ q`
` ~ ( p vv q) cong p ^^ ~ q`
` ~ ( p to ( q ^^ r) cong p ^^ ( ~ ( q ^^ r))`
` cong p ^^ ( ~ q vv ~ r) `[ By De' Morgan's laws]
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OBJECTIVE RD SHARMA ENGLISH-MATHEMATICAL REASONING -Section I - Solved Mcqs
  1. The proposition (p to ~p) ^^ (~p to p) is a

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  2. Which of the following statements is a tautology?

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  3. Negation of the statement pto(q^^r) is

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  4. Negation of the statement (p ^^ r) -> (r vv q) is-

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  5. The negation of the propostion q vv ~ ( p ^^ r) is

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  6. Which of the following is always true ?

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  7. Negation of the statement ~ p to (q vv r) is

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  8. The negation of the propostion " if a quadrillatcral is a square, then...

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  9. The contrapositive of (pvvq) to r is

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  10. The contrapositive of p to ( ~ q to ~ r) is

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  11. The contrapositive of the statement "if 2^(2) =5 then I get first cla...

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  12. If x = 5 and y = -2 , then x -2y =9, the contrapositive of this propos...

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  13. The diagonals of a rhombus are perpendicular. The contrapositive of th...

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  14. Which of the following is wrong?

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  15. The symbolic form of logic of the circuit given below is : (RDSMATH...

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  16. Which of the following statements is a tautology ?

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  17. The statement p to(q to p) is equivalent to

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  18. Let S be non-empty subset of R. consider the following statement: P:...

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  19. Consider the following statements P: Suman is brilliant Q: Suman i...

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  20. The only statement among the following i.e. a tautology is

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