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

(ix) This sentences is a statement.

(x) Is the earth round?

Asked by Aaryan | 1 year ago |  51

##### 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 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) 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 an interrogative sentence.

∴ It is not a statement.

Answered by Sakshi | 1 year ago

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