Membership

Definition

Membership tells whether an object belongs to a set.

Example:

Set: {1, 2, 3}
Object: 2

Since 2 is in the set:

2 is a member of {1, 2, 3}

Membership = belongs to a set.

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Member vs Non-Member

Example set:

A = {1, 2, 3}

Member:

2 belongs to A

Non-member:

5 does not belong to A

The membership question is yes-or-no:

Is this object in this set?

Membership is a truth-valued relationship between object and set.

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Membership Depends On The Set

The same object can be a member of one set and not another.

Example:

A = {1, 2, 3}
B = {4, 5, 6}

The object 2 belongs to A.

It does not belong to B.

Membership is relative to a specific set.

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Membership And Predicates

Membership can be understood as a predicate.

Example:

InSet(x, A)

This asks:

Is x a member of A?

For:

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

the answer is:

true

Membership connects set structure to logical truth.

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Final Summary

• Membership tells whether an object belongs to a set.
• An object can be a member or non-member.
• Membership depends on the specific set.
• Membership is a yes-or-no relation.
• Membership connects sets to predicates and truth values.