Basics of sets

Describe sets using clear membership criteria and distinguish the empty set and subsets.

Meaning

A set is a collection with a clear rule for deciding which objects belong. The objects are called elements. A set is a subset of another set if all its elements also belong to that other set.

Example

If then 4 is an element of A, and is a subset of A. The empty set, which has no elements, is a subset of every set.A set is not a subset of another if it has an element absent from that other set. The empty set has no such element, so it is a subset of every set.The element 4 and the set are different. Distinguish membership from the subset relationship.

Practice for this concept

Scope and references

Topics

Sets, elements, set notation, the empty set, subsets

Learning goal

Describe sets using clear membership criteria and distinguish the empty set and subsets.

Helpful background

Group objects by a condition and decide whether each belongs.

Basic set concepts

These choice exercises use specified finite sets, conditions, or proof steps. They do not establish constructing new counterexamples or proofs, or mastery of the whole logic area.

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