Answer: The statement: If x is an integer and x2 is odd, then x is odd. Contrapositive: If x is even, then x2 is even.
Determine the Contrapositive of each of the following statement: If x is an integer and x2 is odd, then x is odd.
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Exercise 31.5
Determine the Contrapositive of each of the following statements: (i) It is necessary to be strong in order to be a sailor. (ii) Only if he does not tire will he win.
Answers: (i) Contrapositive: If he is not strong, then he is not a sailor (ii) Contrapositive: If he tries, then he will not win.
Determine the Contrapositive of each of the following statements: (i) If x is less than zero, then x is not positive. (ii) If he has courage he will win.
Answers: (i) Contrapositive: If x is positive, then x is not less than zero. (ii) Contrapositive: If he does not win, then he does not have courage.
Determine the Contrapositive of each of the following statements: (i) It never rains when it is cold. (ii) If Ravish skis, then it snowed.
Answers: (i) Contrapositive: If it rains, then it is not cold. (ii) Contrapositive: If it did not snow, then Ravish will not ski.
Determine the Contrapositive of each of the following statements: (i) If she works, she will earn money. (ii) If it snows, then they do not drive the car.
Answers: (i) Contrapositive: If she does not earn money, then she does not work. (ii) Contrapositive: If then they do not drive the car, then there is no snow.
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.
Answers: (i) Contrapositive: If Mohan is not poor, then he is not a poet. (ii) Contrapositive: If Max does not study, then he will not pass the test.
Rewrite each of the following statements in the form “p if and only is q.” (i) r: For you to get an A grade, it is necessary and sufficient that you do all the homework you regularly. (ii) s: If a tumbler is half empty, then it is half full, and if a tumbler is half full, then it is half empty.
Answers: (i) In the form “p if and only is q.” You get an A grade if and only if you do all the homework regularly. (ii) In the form “p if and only is q.” A tumbler is half empty if and only if it...
Rewrite each of the following statements in the form “p if and only is q.” (i) p: If you watch television, then your mind is free, and if your mind is free, then you watch television. (ii) q: If a quadrilateral is equiangular, then it is a rectangle, and if a quadrilateral is a rectangle, then it is equiangular.
Answers: (i) In the form “p if and only is q.” You watch television if and only if your mind is free. (ii) In the form “p if and only is q.” A quadrilateral is a rectangle if and only if it is...
State the converse and contrapositive of each of the following statement: If a quadrilateral is a parallelogram, then its diagonals bisect each other.
Answer: Converse: If the diagonals of a quadrilateral bisect each other, then it is a parallelogram. Contrapositive: If the diagonals of a quadrilateral do not bisect each other, then the...
State the converse and contrapositive of each of the following statements: (i) A positive integer is prime only if it has no divisions other than 1 and itself. (ii) If you live in Delhi, then you have winter clothes.
Answers: (i) Converse: If an integer has no divisor other that 1 and itself, then it is prime. Contrapositive: If an integer has some divisor other than 1 and itself, then it is prime. (ii) ...
State the converse and contrapositive of each of the following statements: (i) If it is hot outside, then you feel thirsty. (ii) I go to a beach whenever it is a sunny day.
Answers: (i) Converse: If you feel thirsty, then it is hot outside. Contrapositive: If you do not feel thirsty, then it is not hot outside. (ii) Converse: If I go to a beach, then it is a sunny...
Write each of the following statements in the form “if p, then q.” (i) Whenever it rains, it is cold. (ii) It never rains when it is cold.
Answers: (i) In the form “if p, then q.” If it rains, then it is cold. (ii) In the form “if p, then q.” If it is cold, then it never rains.
Write each of the following statements in the form “if p, then q.” (i) The game is canceled only if it is raining. (ii) It rains only if it is cold.
Answers: (i) In the form “if p, then q.” If it is raining, then the game is canceled. (ii) In the form “if p, then q.” If it rains, then it is cold.
Write each of the following statements in the form “if p, then q.” (i) It is necessary to have a passport to log on to the server. (ii) It is necessary to be rich in order to be happy.
Answers: (i) In the form “if p, then q.” If you log on the server, then you must have a passport. (ii) In the form “if p, then q.” If he is happy, then he is rich.
Write each of the following statements in the form “if p, then q.” (i) You can access the website only if you pay a subscription fee. (ii) There is traffic jam whenever it rains.
Answers: (i) In the form “if p, then q.” If you access the website, then you pay a subscription fee. (ii) In the form “if p, then q.” If it rains, then there is a traffic jam.