Element Math Example 3

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

Example 3

easy
Let S={1,2,3,4,5}S = \{1, 2, 3, 4, 5\}. Fill in each blank with ∈\in or ∉\notin: (a) 3  □  S3 \;\square\; S, (b) 6  □  S6 \;\square\; S, (c) 0  □  S0 \;\square\; S.

Solution

  1. 1
    (a) 33 is listed in SS, so 3∈S3 \in S.
  2. 2
    (b) 66 is not listed in SS, so 6∉S6 \notin S.
  3. 3
    (c) 00 is not listed in SS, so 0∉S0 \notin S.

Answer

(a)  3∈S,(b)  6∉S,(c)  0∉S(a)\;3 \in S,\quad (b)\;6 \notin S,\quad (c)\;0 \notin S
Membership in a set is determined by whether the element appears in the set's definition or listing.

About Element

An individual object that belongs to, or is a member of, a given set — either it is in the set or it is not.

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More Element Examples

Example 1 easy

Let [formula]. Determine whether [formula], [formula], and [formula].

Example 2 medium

Let [formula]. Which of the following are true? (a) [formula], (b) [formula], (c) [formula], (d) [fo

Example 4 medium

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

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Related Concepts

SetSubset