Subset Concepts

Subset Proper Subset Improper Subset

Subset Theory Quiz

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Subset Quiz Proper Subset Quiz Improper Subset Quiz

Subset (⊆)

A set A is a subset of set B if all elements of A are also elements of B.

Notation: A ⊆ B

Example: If A = {1, 2} and B = {1, 2, 3, 4}, then A ⊆ B.

Proper Subset (⊂)

A set A is a proper subset of set B if all elements of A are in B, but B has at least one element not in A.

Notation: A ⊂ B (some texts use ⊆ with A ≠ B)

Example: If A = {1, 2} and B = {1, 2, 3}, then A ⊂ B.

Improper Subset

An improper subset is either the set itself or the empty set.

Notation: When A ⊆ B and either A = B or A = ∅

Example: For set B = {1, 2, 3}, the improper subsets are: ∅ and {1, 2, 3}

If A = {1, 2} and B = {1, 2, 3}, which statement is true?

A is a subset of B B is a subset of A A and B are equal sets A is not a subset of B

Which of these is a proper subset of {a, b, c}?

{a, b, c} {a, b} {a, b, c, d} { } (empty set only)

How many improper subsets does a set have?

0 1 2 Depends on the set size