Class 11

Math

JEE Main Questions

Mathematical Reasoning

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

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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.

State the converse and contrapositive of the following statement: I go to a beach whenever it is a sunny day.

Write the negation of the following statement: The earth is round.

Write the negation of the following compound statement: Square of an integer is positive or negative.

Are the following pairs of statements negations of each other?(i) The number $x$ is not a rational numberThe number $x$ is not an irrational number(ii) The number $x$ is a rational numberThe number $x$ is an irrational number

Write the negation of the following statement: $r:$ There exists a number $x$ such that $0<x<1.$

Given below are two statement: $p:$ 25 is a multiple of 5. $q:$ 25 is a multiple of 8. Write the compound statement using connective "OR" and check its validity.

Write the component statements of the following compound statements and check whether the compound statement is true or false.(i) A line is straight and extends indefinitely in both directions.(ii) 0 is less than every positive integer and every negative integer.(iii) All living things have two legs and two eyes.