Class 11

Math

JEE Main Questions

Mathematical Reasoning

Find out whether the following sentences is a statement or not. Justify your answer: the real number $x$ is less than 2.

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

Verify by the method of contradiction that $7 $ is irrational.

For each of the following compound statements first identify the connecting words and then break it into component statements(i) All rational numbers are real and all real numbers are not complex(ii) Square of an integer is positive or negative(iii) The sand heats up quickly in the Sun and does not cool down fast at night(iv) $x=2$ and $x=3$ are the roots of the equation $3x_{2}−x−10=0$

By giving a counter example, show that the following statement is false. If n is an odd integer, then n is prime.

Write the negation of the following statement: I will not go to school.

Write the following statements in the form if $p$ then $q:$ It is necessary to have a passport to log on to the server.

Rewrite the following statement with if-then in five different ways conveying the same meaning. If a natural number is odd, then its square is also odd.

Write the negation of the following statement: All cats scratch.

Identify the quantifier in the following statements and write the negation of the statements.(i) There exists a number which is equal to its square.(ii) For every real number x, x is less than $x+1$.(iii) There exists a capital for every state in india.