Practice Subset in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

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

Every single thing in $A$ can also be found inside $B$ . Think of $A$ as fitting entirely within $B$ , like a small circle inside a big one.

Showing a random 20 of 50 problems.

Example 1

easy

\{5\} \subseteq \{1, 5, 9\}

Example 2

hard

How many subsets of

\{1, 2, 3, 4, 5\}

have size exactly

3

Example 3

easy

Let

A = \{1, 2, 3, 4, 5\}

and

B = \{2, 4\}

. Determine whether

B \subseteq A

Example 4

easy

Let

A = \{1, 3\}

and

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

. Is

A \subseteq B

? Is

B \subseteq A

Example 5

challenge

A \subseteq B

, prove that

|A| \le |B|

for finite sets.

Example 6

medium

List all subsets of

S = \{a, b, c\}

Example 7

medium

\mathbb{N} \subseteq \mathbb{Z}

? Is

\mathbb{Z} \subseteq \mathbb{N}

Example 8

medium

True or false:

\{1, 2\} \subseteq \{\{1, 2\}, 3\}

Example 9

easy

Let

X = \{1, 2, 3\}

and

Y = \{1, 2, 3, 4, 5\}

. Is

X \subseteq Y

? Is

Y \subseteq X

Example 10

medium

A \subseteq B

and

|B| = 5

, what is the maximum possible

|A|

Example 11

challenge

Prove that the empty set

\emptyset

is a subset of every set

A

Example 12

medium

Given

A = \{x : x \text{ is even, } 0 < x < 10\}

and

B = \{2, 4, 6, 8\}

, is

A = B

Example 13

medium

Given

A = \{1, 2\}

, is

\{1, 2\} \in

the power set of

A

, and is

\{1, 2\} \subseteq A

Example 14

medium

How many subsets does

\{1, 2, 3\}

have?

Example 15

medium

How many subsets of

\{1, 2, 3, 4\}

are there?

Example 16

hard

How many subsets of

\{1, 2, \dots, 10\}

contain at least one odd number?

Example 17

easy

A = \{1, 2\}

a subset of

B = \{1, 2, 3\}

Example 18

medium

List all subsets of

\{1, 2\}

that contain

1

Example 19

easy

A = \{1, 2, 3\}

a subset of itself?

Example 20

easy

Is the set of even integers a subset of the set of integers?

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Related Concepts

Set Element