# NCERT Class 11-Math's: Chapter –14 Mathematical Reasoning Part 5

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**Question 4:**

Write the truth value of each of the following statements.

(i) is an even integer or is even.

(ii) or

(iii) Delhi is the capital of India and Islamabad is the capital of Pakistan.

(iv) Every rectangle is a square and every square is a rectangle.

(v) The sun is a star or sun is a planet.

**Answer:**

In view of and , we observe that only statement (iv) has truth value F as the first component statement namely “every rectangle is a square” is false.

Further, in statements (i), (ii) and (v) atleast one component statement is true. Therefore, these statements have truth value T.

Also, truth value of statement (iii) is T as both the component statements are true.

**Question 5:**

Write negation of the statement

“Everyone who lives in India is an Indian”

**Answer:**

Let Everyone who lives in India is an Indian. The negation of this statement is given by

It is false that everyone who lives in India is an Indian.

Everyone who lives in India is not an Indian.

**Question 6:**

Write the negation of the following statements:

(a) All triangles are equilateral triangles.

(b) is a multiple of .

(c) A triangle has four sides.

**Answer:**

(a) We have

It is false that all triangles are equilateral triangles

Or

Threre exists a triangle which is not an equilateral triangles.

or

Not all triangles are equilateral triangles

(b)is not a multiple of .

(c) It is false that the triangle has four sides.

or

A triangle has not four sides.

**Question 7:**

Write the negation of the following statements:

(i) Suresh lives in Bhopal or he lives in Mumbai.

(ii) and is a prime number.

**Answer:**

(i) Let

Suresh lives in Bhopal

and Suresh lives in Mumbai

Then the disjunction in (i) is given by .

Now : Suresh does not live in Bhopal.

Suresh does not live in Mumbai.

Therefore, using , negation of is given by

: Suresh does not live in Bhopal and he does not live in Mumbai.

(ii) Let

And is a prime number.

Then the conjunction in (ii) is given by .

Now

And is not a prime number.

Therefore, using , negation of is given by,

is not a prime number.