Class 11

Math

JEE Main Questions

Mathematical Reasoning

Find out whether the following sentence is a statement or not. Justify your answer: All real numbers are complex numbers.

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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

Check whether the following pair of statements are negation of each other. Give reasons for your answer.(i) $x+y=y+x$is true for every real numbers x and y.(ii) There exists real numbers x and y for which \displaystyle{x}+{y}={y}+

Rewrite the following statements in the form $p$ if only if$q:$ if you watch television then your mind is free and if your mind is free, then you watch television.

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.

Show that the following statement is true: The integer $n$ is even if and only if $n_{2}$ is even

Which of the following statements are true and which are false? In each case give a valid reason for saying so(i) p : Each radius of a circle is a chord of the circle(ii) q : The centre of a circle bisects each chord of the circle(iii) r : Circle is a particular case of an ellipse(iv) s : If x and y are integers such that $x>y$ then $−x<−y$(v) t : $11 $ is a rational number

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: All policemen are thieves.