Question

How do you determine the number of elements in a set?

Short answer

Answer: To determine the number of elements in a set, you need to count each unique element while ignoring any repeated elements. An empty or null set has zero elements.

Step-by-step solution

Understanding what a set is

A set is a collection of distinct objects, called elements. The order of these elements does not matter, and each element should appear only once in the set. For example, consider a set of natural numbers A = {1, 2, 3, 4, 5}. In this set, there are 5 unique elements.

Counting the elements in the set

To determine the number of elements in a set, simply count each unique element. For example, in the set A = {1, 2, 3, 4, 5}, there are 5 elements.

Dealing with repeated elements

Remember that a set cannot have duplicate elements. If you encounter any repeated elements while counting, ignore them. For example, if the given set is B = {1, 2, 2, 3, 3, 3, 4, 5}, the correct set representation should be B = {1, 2, 3, 4, 5}. The number of elements in set B is 5, just like in set A.

Handling empty sets

An empty set, also known as the null set, is a set with no elements. It is represented by the symbol ∅ or {}. The number of elements in an empty set is 0.