Subset Math Example 4

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

Example 4

easy

Let

A = \{1, 3\}

and

B = \{1, 2, 3, 4\}

. Is

A \subseteq B

? Is

B \subseteq A

Solution

1
Every element of $A$ (namely 1 and 3) is in $B$ , so $A \subseteq B$ is true.
2
But 2 and 4 are in $B$ and not in $A$ , so $B \subseteq A$ is false.

Answer

A \subseteq B \text{ is true, but } B \subseteq A \text{ is false.}

To test whether one set is a subset of another, check every element of the first set. The direction matters: one true subset relation does not imply the reverse relation is true.

About Subset

Set $A$ is a subset of set $B$ if every element of $A$ is also an element of $B$ , written $A \subseteq B$ .

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More Subset Examples

Example 1 easy

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

Example 2 medium

List all subsets of [formula].

Example 3 easy

Let [formula] and [formula]. Is [formula]? Is [formula]?

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Related Concepts

Set Element