Which of the following sets are finite and which are infinite: 3 (i) The set of the natural numbers divisible by 2. (ii) The set of natural numbers less than 10. (iii) The set of lines passing through a point.

Which of the Following Sets Are Finite and Which Are Infinite?

To determine whether a set is finite or infinite, we check the number of elements in the set.

• A finite set has a fixed number of elements.
• An infinite set has unlimited elements.

(i) The Set of Natural Numbers Divisible by 2

The natural numbers divisible by 2 are:

{2, 4, 6, 8, 10, 12, ...}

This set continues forever because there is no largest even natural number.

Therefore, this set is an Infinite Set.

(ii) The Set of Natural Numbers Less Than 10

The natural numbers less than 10 are:

{1, 2, 3, 4, 5, 6, 7, 8, 9}

This set has only 9 elements.

Therefore, this set is a Finite Set.

(iii) The Set of Lines Passing Through a Point

Through a single point, infinitely many lines can be drawn in different directions.

There is no limit to the number of possible lines.

Therefore, this set is an Infinite Set.

Final Answer

• (i) Infinite Set
• (ii) Finite Set
• (iii) Infinite Set

Conclusion

Finite sets contain limited elements, while infinite sets continue without end.

Understanding this concept helps build a strong foundation in set theory and mathematics.