# Class 11 NCERT Solutions – Chapter 14 Mathematical Reasoning – Exercise 14.1

**Question 1. Which of the following sentences are statements? Give reasons for your answer?**

Note: A sentence is called mathematically acceptable statement if it is either true or false but not both.

**(i) There are 35 days in a month.**

**Solution:**

Yes, this is a statement because there can be 28 / 29 / 30 / 31 days in a month but not 35 and therefore this is definitely false.

**(ii) Mathematics is difficult.**

**Solution:**

No, this is not a statement because for some people math can be easy and for some it is difficult. so it can be both true and false in.

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

**Solution:**

Yes, this is a statement because 5 + 7 = 12, which is greater than 10 and therefore this is definitely true.

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

**Solution:**

No, this is not a statement because square of 3 is 9 which is odd and square of 4 is 16 which is even. so it can be both true and false.

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

**Solution:**

No , this is not a statement because square is a quadrilateral which has all sides equal but for rectangle which is also a quadrilateral in which all sides are not equal. so it can be both true and false.

**(vi) Answer this question.**

**Solution:**

No, this is not a statement because this an order and we cannot say whether it is true or false.

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

**Solution:**

Yes , this is a statement because product of -1 and 8 is -8 and therefore this is definitely false.

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

**Solution:**

Yes, this is a statement because sum of all interior triangle is 180° in a triangle and therefore this is definitely true.

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

**Solution:**

No, this is not a statement because a day can be either windy or not windy we cannot say whether it is true or false.

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

**Solution:**

Yes , this is a statement because all real numbers are complex with imaginary part as 0 and therefore this is definitely true.

**Question 2. Give three examples of sentences which are not statements. Give reasons for the answers?**

**Solution:**

- How far is Chennai from here? This is a question which also contains the word “Here”. Hence it is not a statement
- Tomorrow is Friday. This sentence can either be true or false hence it is not a statement.
- The sum of x and y is greater than 0 .Here, we are not in a position to determine whether it is true or false, unless we know what x and y are and therefore this is not a statement.