State whether the “Or” used in the following statements is “exclusive “or” inclusive. Give reasons for your answer.

**(i) **Sun rises or Moon sets.

**(ii)** To apply for a driving licence, you should have a ration card or a passport.

**(iii)** All integers are positive or negative.

Asked by Pragya Singh | 2 years ago | 160

**(i)** It is not possible for the Sun to rise and the Moon to set together. Hence, the ‘or’ in the given statement is exclusive.

**(ii)** Since a person can have both a ration card and a passport to apply for a driving license. Hence, the ‘or’ in the given statement is inclusive.

**(iii)** Since all integers cannot be both positive and negative. Hence, the ‘or’ in the given statement is exclusive.

Determine whether the argument used to check the validity of the following statement is correct: p: “If x^{2} is irrational, then x is rational.” The statement is true because the number x^{2} = π^{2} is irrational, therefore x = π is irrational.

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 bisect 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: \( \sqrt{11}\) is a rational number.

By giving a counter example, show that the following statement is not true. p: “If all the angles of a triangle are equal, then the triangle is an obtuse angled triangle.”

Show that the following statement is true “The integer n is even if and only if n^{2} is even”

Show that the following statement is true by the method of the contrapositive p: “If x is an integer and x^{2} is odd, then x is also odd.”