Class 11

Math

JEE Main Questions

Mathematical Reasoning

Check whether the following sentence is a statement. Give reasons for your answer: Every set is a finite set.

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Write the component statements of the following compound statements and check whether the compound statement is true or false: (i) Square of an integer is positive or negative (ii) $x=2andx=3$ are the roots of the equation $3x_{2}−x−10=0$ (iii) The sand heats up quickly in the sun and does not cool down fast at night.

Write the negation of the following statement: I went to my class yesterday.

Show that the following statement is true by the method of contrapositive. p: If x is an integer and $x_{2}$is even, then x is also even.

Consider the following sentence: The sun is a star. Is it a statement?

Write the negation of each of the following statements: (i)There exists a capital for every state in India. (ii)There exists a number which is equal to its square.

Write the negation of the following statement: All primes are odd.

Write the negation of the following statement: It rained on July 4, 2005.

Show that the statement For any real numbers a and b, $a_{2}=b_{2}$implies that $a=b$ is not true by giving a counter-example.