# NCERT Class 11-Math՚s: Chapter – 14 Mathematical Reasoning Part 6 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 8:

Rewrite each of the following statements in the form of conditional statements:

(i) Mohan will be a good student if he studies hard.

(ii) Ramesh will get dessert only if he eats his dinner.

(iii) When you sing, my ears hurt.

(iv) A necessary condition for Indian team to win a cricket match is that the selection committee selects an all-rounder.

(v) A sufficient condition for Tara to visit New Delhi is that she goes to the Rashtrapati Bhawan.

(i) The given statement is of the form “q if p” , where

Mohan studies hard.

He will be a good student.

It is an equivalent form (Remark (b) 14.1. 12) of the statement “if p then q” . So the equivalent formulation of the given statement is

“If Mohan studies hard, then he will be a good student” .

(Here, note that in p he is replaced by Mohan and in q Mohan is replaced by he)

(ii) The given statement is of the form

only if ” which is an equivalent form (Remark (c) 14.1. 12) of the statement “if then ” . So, the equivalent formulation of the given statement is:

“If Ramesh eats his dinner, then he will get dessert”

(iii) Here ‘when’ means the same as ‘if’ and so the equivalent formulation of the given statements is:

“If you sing, then my ears hurt”

(iv) The given statement is of the form “ is necessary for ” where

: Indian team wins a cricket match

: The selection committee selects an all-rounder

Which is an equivalent form (Remark (e) 14.1. 12) of “if p then q” . So the equivalent formulation of the given statement is

″ If the teams-wins a cricket match then selection committee selects an all-rounder.

(v) The given statement is of the form “p is sufficient for q” where

: Tara goes to Rashtrapati Bhawan

: She visits New Delhi

Which is an equivalent form (Remark (d) 14.1. 12) of “if , then ” , so the equivalent formulation of the given statement is

“If Tara goes to Rashtrapati Bhawan, then she visits New Delhi” .

Question 9:

Express in English, the statement , where

It is raining today

The conditional statement is

“If it is raining today, then ” .

Question 10:

Translate the following statements in symbolic form:

If and ″ then .

Let and and

Then the given statement is symbolic form is

Question 11:

Form the biconditional of the following statements:

Today is 14th of August

Tomorrow is Independence day

The biconditional is given by

“Today is 14th of August if and only if tomorrow is Independence Day” .

Question 12:

Translate the following biconditional into symbolic form:

“ABC is an equilateral triangle if and only if its each interior angle is

Let ABC is an equilateral triangle

And Each interior angle of triangle ABC is

Then the given statement in symbolic form is .

Question 13:

Identify the quantifiers and write the negation of the following statements

(i) There exists a number which is equal to its square.

(ii) For all even integers , is also even.

(iii) There exists a number which is a multiple of and .

(i) The quantifier is “there exists” and the negation is

“There does not exist a number which is equal to its square”

(ii) The quantifier is “for all” and the negation is

“There exists an even integer x such that is not even”

(iii) The quantifier is “there exists” and the negation is

“There does not exist a number which is a multiple of both and ” .

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