Difference

Definition

The difference between two sets keeps the elements that are in the first set but not in the second.

Example:

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

Difference:

A minus B = {1}

Difference removes from the first set anything found in the second set.

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Order Matters

Set difference is directional.

Example:

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

Then:

A minus B = {1}
B minus A = {4}

These are not the same.

Difference depends on which set comes first.

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Difference vs Intersection

Intersection keeps what two sets share.

Difference removes what they share from the first set.

Example:

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

Intersection:

{2, 3}

Difference:

A minus B = {1}

Intersection finds overlap; difference removes overlap from one side.

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Difference As Filtering

Set difference can be understood as filtering.

Example:

All = {1, 2, 3, 4, 5}
Remove = {2, 4}

Difference:

All minus Remove = {1, 3, 5}

Difference keeps only elements that pass the "not in the second set" test.

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Final Summary

• Difference keeps elements in the first set that are not in the second.
• Set difference is directional.
• A minus B may differ from B minus A.
• Difference is different from intersection.
• Difference can be understood as filtering by non-membership.