RD Sharma Class 11 Solutions Chapter 31 Exercise 31.1 (Updated for 2021-22)

RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.1: We will learn some basics of mathematical reasoning in this exercise. In the context of mathematics, reasoning is a process. Students can use RD Sharma Class 11 Solutions to help them get good grades in their board exams. The pdf of RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.1 is available in the links below, which may be readily downloaded and saved for future reference.

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RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.1

Access answers to RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.1- Important Question with Answers

1. Find out which of the following sentences are statements and which are not. Justify your answer.
(i) Listen to me, Ravi!

(ii) Every set is a finite set.

(iii) Two non-empty sets have always a non-empty intersection.

(iv) The cat’s pussy is black.

(v) Are all circles round?

(vi) All triangles have three sides.

(vii) Every rhombus is a square.

(viii) x² + 5|x| + 6 = 0 has no real roots.

(ix) This sentence is a statement.

(x) Is the earth round?

Solution:

(i) Listen to me, Ravi!

The sentence “Listen to me, Ravi! “Is an exclamatory sentence.

∴ It is not a statement.

(ii) Every set is a finite set.

This sentence is always false because there are sets that are not finite.

∴ It is a statement.

(iii) Two non-empty sets have always a non-empty intersection.

This sentence is always false because there are non-empty sets whose intersection is empty.

∴ It is a statement.

(iv) The cat’s pussy is black.

Some cats are black, and not black, So, the given sentence may or may not be true.

∴ It is not a statement.

(v) Are all circles round?

The given sentence is interrogative.

∴ It is not a statement.

(vi) All triangles have three sides.

The given sentence is a true declarative sentence.

∴ It is a true statement.

(vii) Every rhombus is a square.

This sentence is always false because Rhombuses are not square.

∴ It is a statement.

(viii) x² + 5|x| + 6 = 0 has no real roots.

Firstly, let us solve the given expression.

If x>0,

x²+5|x|+6=0

x²+5x+6=0

x = -3 or x = -2

Since x>0, the equation has no roots.

If x<0,

x²+5|x|+6=0

x² – 5x+6=0

Since x<0, the equation has no real roots.

∴ It is a statement.

(ix) This sentences is a statement.

The statement is not indicating the correct value, hence we can say that value contradicts the sense of the sentence.

∴ It is not a statement.

(x) Is the earth round?

The given sentence is interrogative.

∴ It is not a statement.

Mathematical Reasoning Ex 31.1 Q1 (xi)

Mathematical Reasoning Ex 31.1 Q1 (xii)
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Mathematical Reasoning Ex 31.1 Q1 (xiii)

Mathematical Reasoning Ex 31.1 Q1 (xiv)

Mathematical Reasoning Ex 31.1 Q1 (xv)

Mathematical Reasoning Ex 31.1 Q1 (xvi)

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

Solution:

a) “We won the match!”

The sentence “We won the match!” Is an exclamatory sentence.

∴ It is not a statement.

b) Can u get me a cup of tea?

This sentence is interrogative.

∴ It is not a statement.

c) Please get me the book which is kept on the table.

This sentence is expressed either as a request or as a command, hence it is an imperative sentence.

∴ It is not a statement.

We have provided complete details of RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.1. If you have any queries related to CBSE Class 11, feel free to ask us in the comment section below.

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