RD Chapter 31- Mathematical Reasoning Ex-31.2 |
RD Chapter 31- Mathematical Reasoning Ex-31.3 |
RD Chapter 31- Mathematical Reasoning Ex-31.4 |
RD Chapter 31- Mathematical Reasoning Ex-31.5 |
RD Chapter 31- Mathematical Reasoning Ex-31.6 |

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 pussy is black.

(v) Are all circles round?

(vi) All triangles have three sides.

(vii) Every rhombus is a square.

(viii) x^{2} + 5|x| + 6 = 0 has no real roots.

(ix) This sentences is a statement.

(x) Is the earth round?

**Answer
1** :

(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 which 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 pussy is black.

There are some cats which 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 an interrogative sentence.

∴ 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 a square.

∴ It is a statement.

**(viii) **x^{2} +5|x| + 6 = 0 has no real roots.

Firstly, let us solve the given expression.

If x>0,

x^{2}+5|x|+6=0

x^{2}+5x+6=0

x = -3 or x = -2

Since x>0, the equation has no roots.

If x<0,

x^{2}+5|x|+6=0

x^{2} – 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 an interrogative sentence.

∴ It is not a statement.

**Answer
2** :

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 cup of tea?

This sentence is an interrogative sentence.

∴ 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.

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