Determine the Contrapositive of each of the following statements:

**(i) **If Mohan is a poet, then he is poor.

**(ii) **Only if Max studies will he pass the test.

**(iii)** If she works, she will earn money.

**(iv) **If it snows, then they do not drive the car.

**(v) **It never rains when it is cold.

**(vi)** If Ravish skis, then it snowed.

**(vii) **If x is less than zero, then x is not positive.

**(viii) **If he has courage he will win.

**(ix)** It is necessary to be strong in order to be a sailor.

**(x)** Only if he does not tire will he win.

**(xi)** If x is an integer and x^{2} is odd, then x is odd.

Asked by Aaryan | 1 year ago | 42

**(i)** If Mohan is a poet, then he is poor.

Contrapositive: If Mohan is not poor, then he is not a poet.

**(ii)** Only if Max studies will he pass the test.

Contrapositive: If Max does not study, then he will not pass the test.

**(iii)** If she works, she will earn money.

Contrapositive: If she does not earn money, then she does not work.

**(iv)** If it snows, then they do not drive the car.

Contrapositive: If then they do not drive the car, then there is no snow.

**(v)** It never rains when it is cold.

Contrapositive: If it rains, then it is not cold.

**(vi)** If Ravish skis, then it snowed.

Contrapositive: If it did not snow, then Ravish will not ski.

**(vii)** If x is less than zero, then x is not positive.

Contrapositive: If x is positive, then x is not less than zero.

**(viii)** If he has courage he will win.

Contrapositive: If he does not win, then he does not have courage.

**(ix)** It is necessary to be strong in order to be a sailor.

Contrapositive: If he is not strong, then he is not a sailor

**(x)** Only if he does not tire will he win.

Contrapositive: If he tries, then he will not win.

**(xi)** If x is an integer and x^{2} is odd, then x is odd.

Contrapositive: If x is even, then x^{2} is even.

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.”