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.