Question 1: Write each of the following statements in the form “if p, then q”.

Answer:

(i) You can access the website only if you pay a subscription fee.

*If you pay a subscription fee, then you can access the website.*

(ii) There is traffic jam whenever it rains.

*If it rains, then there is a traffic jam.*

(iii) It is necessary to have a passport to log on to the server

*If you want to log on to the server, then you need a passport.*

(iv) It is necessary to be rich in order to be happy.

*If you want to be happy, then you will have to be rich.*

(v) The game is cancelled only if it is raining.

*If it rains, only then the game is cancelled.*

(vi) It rains only if it is cold.

*If it rains, then it is cold.*

(vii) Whenever it rains it is cold.

*If it rains, then it is cold.*

(viii) It never rains when it is cold.

*If it is cold, then it never rains.*

Question 2: state the converse and contrapositive of each of the following statements:

Answer:

(i) If it is hot outside, then you feel thirsty.

Converse of the given statement:

*If you feel thirsty, then it is hot outside.*

Contrapositive of the given statement:

*If you do not feel thirsty, then it is not hot outside.*

(ii) I go to beach whenever it is a sunny day.

Converse of the given statement:

*If I go to a beach, then it is a sunny day.*

Contrapositive of the given statement:

*If I do not go to a beach, then it is not a sunny day.*

(iii) A positive integer is prime only if it has no divisors other than 1 and itself.

Converse of the given statement:

*If a positive integer has no divisors other than 1 and itself, then it is a prime number.*

Contrapositive of the given statement:

*If a positive integer has some divisors other than 1 and itself, then it is a not prime number.*

(iv) If you live in Delhi, then you have winter clothes.

Converse of the given statement:

*If you have winter clothes, then you live in Delhi.*

Contrapositive of the given statement:

*If you do not have winter clothes, then you do not line in Delhi.*

(v) If a quadrilateral is a parallelogram, then its diagonals bisect each other.

Converse of the given statement:

*If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.*

Contrapositive of the given statement:

*If the diagonals of a quadrilateral do not bisect each other, then it is not a parallelogram.*

Question 3: Rewrite each of the following statements in the form ‘p if and only if q”.

Answer:

(i) p: If you watch television, then your mind is free and if your mind is free, then watch television.

*You watch television if and only if your mind is free.*

(ii) q: If a quadrilateral is equiangular, then it is a rectangle and if a quadrilateral is a you rectangle, then it is equiangular.

*The quadrilateral is a rectangle if and only if it is equiangular. *

(iii) r : For you to get an A grade, it is necessary and sufficient that you do all the homework you regularly.

*You get an A grade if and only if you do all your homework regularly.*

(iv) s : If a tumbler is half empty, then it is half full and if a tumbler is half full, then it is half empty.

*The tumbler is half empty if and only if the tumbler is half full.*

Question 4: Determine the contrapositive of each of the following statements:

Answer:

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

*If Mohan is not poor, then he is not a poet.*

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

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

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

*If she does not earn money, then she will not work.*

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

*If they do not drive a car, then there is no snow.*

(v) It never rains when it is cold.

*If it rains, it is not cold.*

(vi) If Ravish skis, then it snowed.

*If it did not snow, then Ravish does not ski.*

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

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

(viii) If he has courage he will win.

*If he does not win, then he does not have courage.*

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

*If you are not strong, then you cannot be a sailor.*

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

*If he tires, then he will not win.*

(xi) If is an integer and is odd, then is odd.

*If x is even, then x² is even.*