GSEB Solutions Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.1

Gujarat Board GSEB Textbook Solutions Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.1 Textbook Questions and Answers.

Gujarat Board Textbook Solutions Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.1

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

1. There are 35 days in a month.
2. Mathematics is difficult.
3. The sum of 5 and 7 is greater than 10.
4. The square of a number is an even number.
5. The sides of a quadrilateral have equal lengths.
6. Answer their questions.
7. The product of (- 1) and 8 is 8.
8. The sum of interior angles of a triangle is 180°.
9. Today is a windy day.
10. All real numbers are complex numbers.

Solution:
1. Statement:
It is false to say that month has 35 days.

2. Sentence:
Mathematics may be difficult for one but may be easy for the other.

3. Statement:
It is true that the sum of 5 and 7 is greater than 10.

4. Sentence:
The square of a number may be even or it may be odd.
e.g., 2² = 4 (even), 3² = 9 (odd).

5. Sentence:
A quadrilateral may have equal lengths as it may be a rhombus or a square or the quadrilateral may have unequal sides.

6. Sentence:
It is an order.

7. Statement:
It is false because product of (- 1) and 8 is not 8.

8. Statement:
It is true that sum of interior angles of a triangle is 180°.

9. Sentence:
It is windy day. Which day it is ?

10. Statement:
It is true that all real numbers are complex number of the form a + i.0.

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

1. It is a rainy month. Which month is a rainy month? We cannot say which month is rainy.
2. She is very beautiful. Who is beautiful?
3. You are a brave boy. Who is brave?