 # Chapter 31: Mathematical Reasoning  – Exercise 31.5

## Mathematical Reasoning – Exercise – 31.5 – Q.1

(i) If you access the website, then you pay a subscription fee.

(ii) If it rains, then there is traffic jam.

(iii) If you log on to the server, then you must have a passport.

(iv) If he is happy, then he is rich.

(v) If it is raining, then the game is cancelled.

(vi) If it rains, then it is cold.

(vii) If it rains, then it is cold.

(viii) If it is cold, then it never rains.

## Mathematical Reasoning – Exercise – 31.5 – Q.2

(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 day. Contrapositive: If I do not go to a beach, then it is not a sunny day.

(iii) Converse: If an integer has no divisors other than 1 and itself, then it is prime. Contrapositive: If an integer has some divisors other than 1 and itself, then it is not prime.

(iv) Converse. If you have winter clothes, then you live in Delhi. Contrapositive: If you do not have winter clothes, then you do not live in Delhi.

(v) Converse: If the diagonals of a quadrilateral bisect each other, then is a parallelogram. Contrapositive: If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram.

## Mathematical Reasoning – Exercise – 31.5 – Q.3

(i) You watch television if and only if your mind is free.

(ii) A quadrilateral is a rectangle if and only if it is equiangular.

(iii) You get an A grade if and only if you do all the homework regularly.

(iv) A tumbler is half empty if and only if it is half full.

## Mathematical Reasoning – Exercise – 31.5 – Q.4

(i) If Mohan is not poor, then he is not a poet.

(ii) If Max does not study, then he will not pass the test.

(iii) If she does not earn money, then she does not work.

(iv) If then they do not drive the car, then there is no snow.

(v) If it rains, then it is not cold.

(vi) If it did not mow, then Ravish will not ski.

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

(viii) If he does not win, then he does not have courage.

(ix) If he is not strong, then he is not a sailor.

(x) If he tires, then he will not win.

(xi) If x is even, then x2 is even.

### Course Features

• Video Lectures
• Revision Notes
• Previous Year Papers
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Test paper with Video Solution

r