The statement (p↔ q) is
Determine the contrapositive of each of the following statements: (i)Only if he does not tire will he win I(ii)f x is an integer and x2 is odd, then x is odd (iii)Only if max studies will he pass the test.
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
Write the negation of the following statements:
(i) Chennai is the capital of Tamil Nadu
(ii) 2 is not a complex number
(iii) All triangles are not equilateral triangle
(iv) The number 2 is greater than 7
(v) Every natural number is an integer
Rewrite the following statement with if then in five different ways conveying the same meaning: If a natural number is odd, then its square is also odd.
Are the following pairs of statements are negation of each other: The number x is not a rational number. The number x is an irrational number.
Identify the quantifier in each of the following statements: (i)For every real number x, x+4 is greater then x˙ (ii)There exists a real number which is twice of itself. (iii)There exists a (living) person who is 200 years old. (iv)For every x∈N, x+1>x˙