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Let S be non-empty subset of R. consider...

Let S be non-empty subset of R. consider the following statement:
P: There is a rational number ` x ne S " such that " x gt 0`
Which of the following statements is the negation of the statement P ?

A

Every rational number `x ne S ` such that `x le 0`

B

`x in S and x le 0 Rightarrow x` is not rational

C

There is a rational number `x in S " such that " x le 0`

D

There is no rational number `x in S " such that x le 0`

Text Solution

Verified by Experts

The correct Answer is:
A
We know that the negation of " there exists" is " for every " So, negaion of statement P is statement given in option (a).
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OBJECTIVE RD SHARMA-MATHEMATICAL REASONING -Section I - Solved Mcqs
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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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