# NCERT Class 11 Mathematics Solutions: Chapter 14 –Mathematical Reasoning Miscellaneous Exercise Part 2

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1. Write each of the statements in the form “if ”.

(i) It is necessary to have a password to log on to the server.

(ii) There is traffic jam whenever it rains.

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

Answer: (i)

Statement p can be written as follows.

If you log on to the server, then you have a password.

Answer: (ii)

Statement q can be written as follows.

If it rains, then there is a traffic jam.

Answer: (iii)

Statement r can be written as follows.

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

2. Re write each of the following statements in the form “ if and only if ”.

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

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

(iii) If a quadrilateral is equiangular, then it is a rectangle and if a quadrilateral is a rectangle, then it is equiangular.

Answer: (i)

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

Answer: (ii)

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

Answer: (iii)

A quadrilateral is equiangular if and only if it is a rectangle.

3. Given below are two statements is a multiple of is a multiple of . Write the compound statements connecting these two statements with “And” and “Or”. In both cases check the validity of the compound statement.

Answer:

The compound statement with ‘And’ is “ is a multiple of and ”.

This is a false statement, since is not a multiple of .

The compound statement with ‘Or’ is “ is a multiple of ”.

This is a true statement, since is not a multiple of but it is a multiple of .