1.3 Subsets

4 lessons

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concept

Subsets

Understanding containment

What is a Subset?

Set $A$ is a subset of set $B$ if every element of $A$ is also in $B$ .

Symbol: $A \subseteq B$

Read: " $A$ is a subset of $B$ " or " $A$ is contained in $B$ "

Think: If $B$ is a big box and $A$ is smaller, everything in $A$ must be in $B$ .

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concept

Counting Subsets

The 2^n formula

The Subset Formula

If a set has $n$ elements, it has exactly $2^n$ subsets (including the empty set and the set itself).

Formula: Number of subsets = $2^n$

This is a powerful counting formula!

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interactive

Subset Visualization

See subsets in action

Subset Builder

Problem: List all subsets of {a, b}

To build a subset, decide for each element: in or out?

Tap to build all possible subsets.

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quiz

Check: Subsets

Test subset understanding

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If $A$ has 5 elements, how many proper subsets does it have?

← previous1.2 Types Of Sets next →1.4 Intervals

concept

Subsets

Understanding containment

What is a Subset?

Set $A$ is a subset of set $B$ if every element of $A$ is also in $B$ .

Symbol: $A \subseteq B$

Read: " $A$ is a subset of $B$ " or " $A$ is contained in $B$ "

Think: If $B$ is a big box and $A$ is smaller, everything in $A$ must be in $B$ .

1 / 8

concept

Counting Subsets

The 2^n formula

The Subset Formula

If a set has $n$ elements, it has exactly $2^n$ subsets (including the empty set and the set itself).

Formula: Number of subsets = $2^n$

This is a powerful counting formula!

1 / 7

quiz

Check: Subsets

Test subset understanding

1 / 6

If $A$ has 5 elements, how many proper subsets does it have?