JEE Main Questions
Write the negation of the following statement: 7 is rational.
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 n2>9 (by contradiction method)
Check whether the following statement is true or not. If x, y∈Zare such that x and y are odd, then xy is odd.
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 a and b, a2=b2 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 x3+4x=0. then x is 0 is true by(i) direct method, (ii) method of contradiction,(iii) method of contrapositive.