Set Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Let A={2,4,6,8,10}A = \{2, 4, 6, 8, 10\}. Determine whether 6∈A6 \in A and whether 5∈A5 \in A.

Solution

  1. 1
    Recall that a set is a well-defined collection of distinct objects called elements. The set A={2,4,6,8,10}A = \{2, 4, 6, 8, 10\} is given in roster (list) notation.
  2. 2
    Check membership of 6: scan the roster — 2, 4, **6**, 8, 10. The element 6 appears, so 6∈A6 \in A.
  3. 3
    Check membership of 5: scan the roster — 2, 4, 6, 8, 10. The element 5 does not appear, so 5∉A5 \notin A.

Answer

6∈A and 5∉A6 \in A \text{ and } 5 \notin A
The symbol ∈\in means 'is an element of.' To test membership, check whether the element appears in the set's roster.

About Set

A well-defined collection of distinct, unordered objects called elements, described either by listing or by a membership rule.

Learn more about Set →

More Set Examples

Example 2 medium

Write the set [formula] in roster notation.

Example 3 easy

Let [formula]. List all elements of [formula] and state the cardinality [formula].

Example 4 easy

Are the sets [formula] and [formula] equal? Explain.

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