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

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Converse, Inverse and Contrapositive Statements are shown.

Converse, Inverse and Contrapositive Statements

Converse, Inverse and Contrapositive Statements are shown.

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 .