Content - Subsets, Supersets, and Operations with Sets

Subsets, Supersets,
and Operations with Sets

If every element of a set A is also an element of a set S, then A is a subset of S and S is a superset of A, written as A

S. A more intuitive definition is that a subset is a set drawn from a larger set. For example, if graduates consist of both boys and girls, the boy graduates make up a subset. Another example is {2, 4, 6}

{1, 2, 3, . . . }.

The set "boy graduates" is a subset of all graduates consisting of both boys and girls.

A special set, which contains no elements, is called the empty set and denoted by Ø. The empty set is different from the set that contains a number zero, {0}. The former has no element at all while the latter has an element "0".

Definition of Union: The word union means "united" or "all together." When you combine the elements of set A and the elements of set B, you form a new set C, which is called the union of A and B and denoted by AB.

Definition of Intersection: The intersection of two sets A and B consists of the elements common to both sets, denoted by AB. If A and B have no common elements, AB = Ø, then A and B are said to be disjoint.
Examples: {1, 2, 3} {3, 4, 5} = {3} and {1, 2, 3} {4, 5, 6} = Ø

Equal Sets: When two sets have the exact same members, regardless of the order in which the members are listed, they are said to be equal.
Examples: {1, 2, 3} = {3, 2, 1}

Equivalent Sets: When two sets have the same number of members, they are said to be equivalent.
Examples: {1,2,3} is equivalent to {a,b,c} and this is written as {1,2,3} ~ {a,b,c}.

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