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Negation of the statement (p ^^ r) -> (...

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

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
A
we know that
` ~ ( p to q) cong p ^^ ~ q`
` ~ ((p ^^ r) to ( r vv q)) cong p ^^ ~ q `
` ~( p to ( q ^^r) ) cong ( p ^^ r) ^^ ( ~ ( r vv q))`
` cong ( p ^^ r) ^^ ( ~ r ^^ ~ q)`
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OBJECTIVE RD SHARMA-MATHEMATICAL REASONING -Section I - Solved Mcqs
  1. Which of the following statements is a tautology?

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  2. Negation of the statement p to ( q ^^ r) is

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

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  4. The negation of q vv ~ ( p ^^ r) is

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  5. Which of the following is always true ?

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

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

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  8. The contrapositive of (pvvq) to r is

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

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

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

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

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  13. Which of the following is wrong?

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

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  15. Which of the following statements is a tautology ?

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

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

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

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

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  20. Let p and q be two statements. Amongst the following , the statement t...

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