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 x2 is odd, then x is odd.
(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 x2 is odd, then x is odd.
Contrapositive: If x is even, then x2 is even.
Answered by Sakshi | 1 year agoDetermine whether the argument used to check the validity of the following statement is correct: p: “If x2 is irrational, then x is rational.” The statement is true because the number x2 = π2 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 n2 is even”
Show that the following statement is true by the method of the contrapositive p: “If x is an integer and x2 is odd, then x is also odd.”