Write the contrapositive and converse of the following statements.

**(i)** If x is a prime number, then x is odd.

**(ii)** It the two lines are parallel, then they do not intersect in the same plane.

**(iii)** Something is cold implies that it has low temperature.

**(iv)** You cannot comprehend geometry if you do not know how to reason deductively.

**(v)** x is an even number implies that x is divisible by 4

Asked by Pragya Singh | 11 months ago | 64

**(i) **Contrapositive: If x is not odd, then x is not a prime number.

Converse: If x is odd, then x is a prime number.

**(ii) **Contrapositive: If two lines intersect in the same plane, then they are not parallel.

Converse: If two lines do not intersect in the same plane, then they are parallel.

**(iii) **Contrapositive: If something does not have low temperature, then it is not cold.

Converse: If something has low temperature, then it is cold.

**(iv) **Contrapositive: If you know how to reason deductively, then you can comprehend geometry.

Converse: If you do not know how to reason deductively, then you cannot comprehend geometry.

**(v) **Contrapositive: If x is not divisible by 4 , then x is not an even number.

Converse: If x is divisible by 4 , then x is an even number

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.”