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