Class 11

Math

JEE Main Questions

Mathematical Reasoning

Write the negation of the following statement: $7 $ is rational.

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Check the validity of the statements given below by the method given against it(i) p : The sum of an irrational number and a rational number is irrational (by contradiction method)(ii) q : If $n$ is a real number with $n>3$ then $n_{2}>9$ (by contradiction method)

Consider the following sentence: May God bless You! Is it a statement?

Check whether the following statement is true or not. If x, $y∈Z$are such that x and y are odd, then xy is odd.

Verify by the method of contradiction. $p:7 $is irrational.

Check whether the following sentence is a statement. Give reasons for your answer: There is no rain without clouds.

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

Show that the statement p: If x is a real number such that $x_{3}+4x=0$. then x is 0 is true by(i) direct method, (ii) method of contradiction,(iii) method of contrapositive.

Check the validity of the statement given below by contradiction method. $p:$ The sum of an irrational number and a rational number is irrational.