Question

Check whether the following sentences are statements.

(i) Answer this question.

(ii) Everyone in this room is rich.

(iii) There is no rain without clouds.

(iv) Mathematics is fun.

(v) She is a commerce graduate.

(vi) $\sqrt{2}$ is a rational number.

(vii) Fire is always hot.

(viii) The sides of a quadrilateral have equal length.

Answer 1

(i) It is an order and therefore, it is not a statement.

(ii) From the context it is not clear which room is referred here and also the term rich is not well defined.

So, the given sentence is not a statement.

(iii) This sentence is always true and therefore, it is a statement.

(iv) For those who like mathematics it may be a fun but for others it may not be.

So, the given sentence cannot be judged to be true or false.

Hence, it is not a statement.

(v) It is not known who she is. So, the given sentence is not a statement.

(vi) Clearly $\sqrt{2}$ is an irrational number. So, the given sentence is false.

Therefore, it is a statement.

(vii) Clearly, the given sentence is always true.

Hence, it is a statement.

(viii) All the sides of a square as well as that of a rhombus are equal. But, the sides of a trpezium as well as that of a rectangle are inequal.

So, the given sentence is sometimes true and sometimes false.

Hence, it is not a statement.