Class 11

Math

JEE Main Questions

Mathematical Reasoning

Consider the following sentence: Please do me a favor. Is it a statement?

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Write the negation of the following statement and check whether the a resulting statement is true: There does not exist a quadrilateral which has all its sides equal.

Is the following is a statement (or proposition)? $x+2=9.$

Is the following a statement (or proposition)? 6 has three prime factors

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

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

Find out whether the following sentence is a statement or not. Justify your answer: Are all circles round?

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

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.