Argument Used: x^{2} = π^{2} is irrational, therefore x = π is irrational.

p: “If x^{2} is irrational, then x is rational.”

Let us take an irrational number given by x =\( \sqrt{k}\), where k is a rational number.

Squaring both sides, we get,

x^{2} = k

x^{2} is a rational number and contradicts our statement.

Hence, the given argument is wrong.

Answered by Aaryan | 1 year agoWhich 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.”

Show that the statement p : “If x is a real number such that x^{3} + x = 0, then x is 0” is true by

**(i) **Direct method

**(ii)** method of Contrapositive

**(iii) **method of contradiction