Set Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Set.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.
Concept Recap
A well-defined collection of distinct, unordered objects called elements, described either by listing or by a membership rule.
Think of a set as a bag that can hold anything — numbers, names, shapes — but with two strict rules: no duplicates allowed and the order in which items sit inside the bag does not matter.
Read the full concept explanation →How to Use These Examples
- Read the first worked example with the solution open so the structure is clear.
- Try the practice problems before revealing each solution.
- Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea: Sets are defined by membership—either something is in or it's not.
Common stuck point: \{1, 2, 3\} = \{3, 1, 2\} (order doesn't matter). \{1, 1, 2\} = \{1, 2\} (no duplicates).
Sense of Study hint: Write out the membership rule in words: 'x is in this set if and only if ___.' If you can fill the blank, you understand the set.
Worked Examples
Example 1
easySolution
- 1 Recall that a set is a well-defined collection of distinct objects called elements. The set A = \{2, 4, 6, 8, 10\} is given in roster (list) notation.
- 2 Check membership of 6: scan the roster — 2, 4, **6**, 8, 10. The element 6 appears, so 6 \in A.
- 3 Check membership of 5: scan the roster — 2, 4, 6, 8, 10. The element 5 does not appear, so 5 \notin A.
Answer
Example 2
mediumPractice Problems
Try these problems on your own first, then open the solution to compare your method.