JEE Main Questions
Check whether the following sentence is a statement. Give reasons for
your answer: Every set is a finite set.
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Write the component statements of the following compound statements and
check whether the compound statement is true or false:
(i) Square of an integer is positive or negative
(ii) x=2 and x=3
are the roots of the equation 3x2−x−10=0
(iii) The sand heats up quickly in the sun and does not cool down fast at
Write the negation of the following statement: I went to my class yesterday.
Show that the following statement is true by the method of contrapositive. p: If x is an integer and x2is even, then x is also even.
Consider the following sentence: The sun is a star. Is it a statement?
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.
Write the negation of the following statement: All primes are odd.
Write the negation of the following statement: It rained on July 4,
Show that the statement For any real numbers a and b, a2=b2implies that a=b is not true by giving a counter-example.