JEE Main Questions
Find the component statement of the following and check whether they are true or not: 24 is a multiple of 2,4, and 8.
Write the component statements of each of the following statements. Also, check whether the statements are true or not. (i)If a triangle ABC is equilateral then it is isosceles. (ii)If a and b are integers, then ab is a rational number.
State whether the Or used in the following statements is exclusive of' inclusive. Give reasons for your answer.(i) Sun rises or Moon sets.(ii) To apply for a driving license, you should have a ration card or a passport.(iii) All integers are positive or negative.
Which of the following sentences are statements? Give reasons for your answer
(i) There are 35 days in a month
(ii) Mathematics is difficult
(iii) The sum of 5 and 7 is greater than 10
(iv) The square of a number is an even number
(v) The sides of a quadrilateral have equal length
(vi) Answer this question
(vii) The product of (−1) and 8 is 8
(viii) The sum of all interior angles of a triangle is 180∘
(ix) Today is a windy day
(x) All real numbers are complex numbers
Write the contrapositive of the following statements: (i)If x is prime number then x is odd (ii)If two lines re parallel then they do not intersect in the same plane. (iii)x is even number implies that x is divisible by 4.
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.
Find out whether the following sentence is a statement or not. Justify your answer: Mathematics is difficult.
Write the converse of the following statements: (i)If two integers a and b are such that a>b then a−b is always a positive integer. (ii)If x is prime number, then x is odd. (iii)If two lines are parallel, then they do not intersect in the same place.