**NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex
14.1**

NCERT Solutions for Class
11 Maths Chapter 14
Mathematical Reasoning Ex 14.1 are the part of NCERT Solutions for Class 11
Maths. Here you can find the NCERT Solutions for Class 11 Maths Chapter 14
Mathematical Reasoning Ex 14.1.

**Ex 14.1 Class 11 Maths Question 1.**

Which of the following sentences are statements? Give reasons for your answer.**(i)**There are 35 days in a month.

**(ii)**Mathematics is difficult.

**(iii)**The sum of 5 and 7 is greater than 10.

**(iv)**The square of a number is an even number.

**(v)**The sides of a quadrilateral have equal length.

**(vi)**Answer this question.

**(vii)**The product of (-1) and 8 is 8.

**(viii)**The sum of all interior angles of a triangle is 180°.

**(ix)**Today is a windy day.

**(x)**All real numbers are complex numbers.

**Solution:**

**(i)** The given sentence is false, because the maximum number of days
in a month can never exceed 31. Therefore, this sentence is a statement.

**(ii)** The given sentence is subjective in the sense that for those
who hate mathematics, it is difficult but for others it may not be difficult.
This means that the given sentence is not always true. Hence, this sentence is
not a statement.

**(iii)** The given sentence is true as the sum of 5 and 7 is greater
than 10. Hence, the given sentence is a statement.

**(iv)** The given sentence is subjective in the sense that it depends
on the number that is being squared. Hence, this sentence is not a statement.

**(v)** The given sentence is sometimes true and sometimes false since
sides in squares and rhombuses have equal length whereas sides in rectangles
and trapeziums have unequal length. Hence, this sentence is not a statement.

**(vi)** The given sentence is an order and so, it is not a statement.

**(vii)** The given sentence is false as the product of (-1) and 8 is
-8. So, the given sentence is a statement.

**(viii)** The given sentence is true and therefore, this sentence is a
statement.

**(ix)** It is not clear from the context which day is referred.
Therefore, the given sentence is not a statement.

**(x)** All real numbers can be written in the form of complex numbers.
So, this sentence is true. Hence, this sentence is a statement.

**Ex 14.1 Class 11 Maths Question
2.**

Give three examples
of sentences which are not statements. Give reasons for the answers.

**Solution: **

**(i)** Who are
you?

The above
sentence is an interrogative sentence. Hence, it is not a statement.

**(ii)** May God
bless you!

The above
sentence is an exclamatory sentence. Hence, it is not a statement.

**(iii)** How are
you?

The above
sentence is an interrogative sentence. Hence, it is not a statement.

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