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Home » Which of the following quantified statement is true? A) The square of every real number is positive B) There exists a real number whose square is negative C) There exists a real number whose square is not positive D) Every real number is rational
Which of the following quantified statement is true?
A) The square of every real number is positive
B) There exists a real number whose square is negative
C) There exists a real number whose square is not positive
D) Every real number is rational
Maths
Which of the following quantified statement is true?
A) The square of every real number is positive
B) There exists a real number whose square is negative
C) There exists a real number whose square is not positive
D) Every real number is rational

Solution:

The correct option is
(A) The square of every real number is positive
Square of every real number is positive, as multiplying negative number two times we get positive number and multiplication of positive number is always positive.
Therefore, there does not exist any real number whose square is negative.
So, \mathrm{B} and \mathrm{C} are incorrect.
And (A) is correct.
\sqrt{2} is an irrational number as it can’t be represented in the form of \frac{\mathrm{p}}{\mathrm{q}}, where \mathrm{p} and q both are integers.
Therefore, D is also incorrect.
As a result, only A is true.

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