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Which of the following is always true ?...

Which of the following is always true ?

A

` ( p to q) cong ( ~ q to ~ p)`

B

`~ ( p vv q) cong ( ~ p vv ~ q)`

C

` ~ ( p to q) cong ( p vv ~ q)`

D

` ~ ( p ^^ q) cong ( ~ p ^^ ~ q)`

Text Solution

Verified by Experts

The correct Answer is:
A
we have
` ~ ( p vv q) cong ( ~ p ^^ ~ q) and , ~( p ^^ q) cong ~ p vv q `
So, options (b) and (d) are not ture.
We know that
` ( p to q) cong ~ p vv q`
` and ~ q to p cong ( ~ ( ~ q) cong ( q vv ~ p) cong ~ p vv q`
`therefore ( p to q) cong ( ~ q to ~ p)`
Hence, option (a) is true.
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OBJECTIVE RD SHARMA-MATHEMATICAL REASONING -Section I - Solved Mcqs
  1. Negation of the statement (p ^^ r) -> (r vv q) is-

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

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  3. Which of the following is always true ?

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

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

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  6. The contrapositive of (pvvq) to r is

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

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

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

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

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  11. Which of the following is wrong?

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

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  13. Which of the following statements is a tautology ?

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

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

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

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

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

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  19. The statement ~(p harr ~q) is

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  20. The negation of ~ svv(~ r^^s) is equivalent to :

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