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

The statement `p to(q to p)` is equivalent to

A

` p to (p ^^q)`

B

`p to ( p harr q)`

C

` p to ( p to q) `

D

` p to ( p vv q)`

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The correct Answer is:
D
we have,
` p to ( q to p)`
`=- p vv ( q to p)`
` = ~ p vv ( ~ q vv p)`
` = ( ~ p vv p) vv ~ q = t vv ~ q =t `
Also, ` p to p to q = ~ -p vv ( p vvq) = (~ p vv p) vv q = t vv q =t`
` p to ( q to p) cong p to ( p vv q)`
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OBJECTIVE RD SHARMA-MATHEMATICAL REASONING -Section I - Solved Mcqs
  1. The contrapositive of p to ( ~ q to ~ r) is

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

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

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

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  5. Which of the following is wrong?

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

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  7. Which of the following statements is a tautology ?

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

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

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

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

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

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

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

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  15. The Bolean Expression ( p ^^ ~ q) vv q vv ( ~ p ^^ q vv ( ~ p ^^ q) ...

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  16. Consider the following statements. p : if 7 is an odd number , then ...

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  17. The negation of A to (A vv ~ B) is

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  18. The following statement (p to q) to [(~p to q) to q] is

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  19. Which of the following is a tautology ?

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  20. The proposition ~p vv( p ^^ ~ q) is equivalent to

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