The negation of the statement -p- For every real number x - x 3- x 2 - - is-A- There exists real number c such that x3-x2-B- There exists real number c such that x2-xC- There exists real number c such that x 3- x-D- There exists a real number x such that x3-x2

The correct option is D There exists a real number x such that x3 lt; x2. The negation of the statement “p: For every real number x, x3 gt; x2.” Is ...

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Standard XI

Mathematics

Common Difference

The negation ...

Question

The negation of the statement “p: For every real number x, x³ > x².” is:

There exists real number c such that x² > x.

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There exists real number c such that x³ > x.

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There exists a real number x such that x³ < x².

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There exists real number c such that x³ = x².

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Solution

The correct option is C
There exists a real number x such that x³ < x².

The negation of the statement “p: For every real number x, x³ > x².” Is “There exists a real number x such that x³ < x²”.

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Similar questions

Q. Write the negation of the following statements:
(i) p : For every positive real number x, the number (x − 1) is also positive.
(ii) q : For every real number x, either x > 1 or x < 1.
(iii) r : There exists a number x such that 0 < x < 1.

Q. Let

R

be the set of real numbers and

f : R \to R

be given by

f (x) = \sqrt{| x |} - log (1 + | x |)

. We now make the following assertions:
I. There exists a real number

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f (x) \leq A

for all

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II. There exists a real number

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f (x) \geq B

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Write the negation of the following statements:

(i) p: For every positive real number x, the number x – 1 is also positive.

(ii) q: All cats scratch.

(iii) r: For every real number x, either x > 1 or x < 1.

(iv) s: There exists a number x such that 0 < x < 1.

Q. For any positive real number x, prove that there exists an irrational number y such that 0 < y < x.

Q. Write the suitable quantifier for there exists a real number x such that

x + 2 = 3

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The negation of the statement “p: For every real number x, x3 > x2.” is:

The correct option is C There exists a real number x such that x3 < x2. The negation of the statement “p: For every real number x, x3 > x2.” Is “There exists a real number x such that x3 < x2”.

The negation of the statement “p: For every real number x, x³ > x².” is:

The correct option is C
There exists a real number x such that x³ < x².

The negation of the statement “p: For every real number x, x³ > x².” Is “There exists a real number x such that x³ < x²”.