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Home  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class11  >>  Mathematical Reasoning

Which of the following is a logical statement?

(1) Are you studying in IIT?

(2) Sum of two irrational numbers is always irrational

(3) Every rectangle is a parallelogram

(4) There are only finitely many real numbers

$\begin{array}{1 1}(A) \text{All are logical statements} \\ (B) \text{Only (2) and (3) are logical statements} \\ (C) \text{Only (2), (3) and (4) are logical statements} \\\text{(D) Only (2) and (4) are logical statements} \end{array}$
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1 Answer

Given

(1) Are you studying in IIT?

(2) Sum of two irrational numbers is always irrational

(3) Every rectangle is a parallelogram

(4) There are only finitely many real numbers

(1) Are you studying in IIT is not a logical statement, it's a question.
(2) Sum of two irrational numbers is always irrational is a logical statement even though its false. We can decide logically if its true or false. For example (1 - $\sqrt 3 + 1- \sqrt 3$) is the sum of two irrational numbers, but its value is $2$ which is a rational number.
(3) Every rectangle is a parallelogram is a logical statement (and true).
(4) There are only finitely many real numbers is a logical statement (but false).
Therefore, (2), (3) and (4) are logical statements.
answered Mar 20, 2014 by balaji.thirumalai
 

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