Set A is a proper subset of set B (A ⊂ B) if all of the elements of set A are members of set B, but there is at least one element of set B that is not an member of set A (A ≠ B).

Since all of the members of set A are members of set D, A is a subset of D. Symbolically this is represented as A ⊆ D.

Note that A ⊆ D implies that n(A) ≤ n(D) (i.e. 3 ≤ 6).

Note that A is also a proper subset of D since set D has members that do not belong to set A (A ≠ D). Symbolically this is represented as A ⊂ D.

Note that A ⊂ D implies that n(A) < n(D) (i.e. 3 < 6).

Since some of the members of set C are NOT members of set D, C is NOT a proper subset of D. Symbolically this is represented as C D.

Since all of the members of set A are members of set B, A is a subset of B. Symbolically this is represented as A ⊆ B.

Although A ⊆ B, since there are no members of set B that are NOT members of set A (A = B), A is NOT a proper subset of B.

Any set is considered to be a subset of itself.

No set is a proper subset of itself.

The empty set is a subset of every set.

The empty set is a proper subset of every set except for the empty set.