Question

Decide whether or not the following are statements. In the case of a statement, say if it is true or false, if possible. Some sets are finite.

Short answer

The statement 'Some sets are finite.' is both a statement and it is true.

Step-by-step solution

Identify if the sentence is a statement

A statement in logic is a declarative sentence which is either true or false, but not both. Looking at the given sentence: 'Some sets are finite.' This sentence is declarative and it can logically either be true or false. Hence, it qualifies as a statement.

Determine the truth value of the statement

The statement is 'Some sets are finite.' In mathematics, a set is defined as a collection of distinct objects, considered as an object in its own right. There are indeed sets that are finite. For instance, the set of natural numbers less than 10, which are {1, 2, 3, 4, 5, 6, 7, 8, 9}, is a finite set. Hence, the statement 'Some sets are finite.' is true.