Intersection

Definition

The intersection of two sets contains the elements that belong to both sets.

Example:

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

Intersection:

A intersection B = {2, 3}

Intersection keeps only shared elements.

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Shared Membership

An object belongs to the intersection only if it belongs to both sets.

Example:

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

2 belongs to both.

3 belongs to both.

1 belongs only to A.

4 belongs only to B.

So:

A intersection B = {2, 3}

Intersection requires membership in both sets.

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Intersection As AND

Intersection is similar to logical AND.

An object belongs to:

A intersection B

if:

it belongs to A AND it belongs to B

Both conditions must hold.

Intersection generalizes AND over set membership.

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Empty Intersection

Two sets may have no shared elements.

Example:

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

Intersection:

{}

The empty set means there are no common elements.

Empty intersection means no overlap.

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Final Summary

• Intersection contains shared elements.
• An element must belong to both sets to be in the intersection.
• Intersection behaves like AND for membership.
• An intersection can be empty.
• Intersection identifies overlap between sets.