Union

Definition

The union of two sets contains every element that belongs to either set.

Example:

A = {1, 2}
B = {2, 3}

Union:

A union B = {1, 2, 3}

Union combines membership from both sets.

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Union Keeps Distinct Elements

The element 2 appears in both sets:

A = {1, 2}
B = {2, 3}

But the union contains it once:

{1, 2, 3}

Sets do not count repeated membership as duplicate elements.

Union follows set membership, not repeated listing.

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Union As OR

Union is similar to logical OR.

An object belongs to:

A union B

if:

it belongs to A OR it belongs to B

Example:

2 belongs to A
2 belongs to B

So 2 belongs to the union.

Union generalizes OR over set membership.

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Why Union Matters

Union lets us combine domains or categories.

Example:

Even = {2, 4, 6}
Odd = {1, 3, 5}

Union:

{1, 2, 3, 4, 5, 6}

This creates a larger collection from smaller collections.

Union builds larger sets from alternatives.

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Final Summary

• Union contains elements from either set.
• Duplicate appearances do not matter.
• Union behaves like OR for membership.
• Union combines domains or categories.
• Union creates a larger set from multiple sets.