Complement of a Set

In this lesson we will learn how to find the complement of a set.

Vocabulary used in this lesson:

• Set
• Complement
• Universal Set
• Null Set
• Empty Set

Definition: The complement of a set is the set of all elements in the universal set that are not in the initial set.

Example:

The complement of the set A in the above picture is set A' indicated in yellow.

Tips:

The union between a set and its complement is the universal set.

The intersection between a set and its complement is the null set.

Example:

If the universal set U = {x: x integer; -6< x <7 } and

M = {y: y even number; 1< y <5}, what is the complement of M?

Solution: First, let's find all elements of sets U and M.

U = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6}; M = {2, 4}

We can also draw a Venn diagram to display sets U, M, and M'.

The complement of set M is a the set highlighted in yellow, whose elements are in set U, but not in set M.

Therefore M' = {-5, -4, -3, -2, -1, 0, 1, 3, 5, 6}.

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