The Complement of a Set

The complement of set A is the set of all the elements that are not in set A, but still in the universal set. We write this as A’.

For example:

U= \left\{1, 2, 3, 4, 5, 6, 7, 8 \right\}

A= \left\{2, 4, 6, 8 \right\}

B= \left\{1, 3, 7, 8 \right\}

Then:

A^{c} = \left\{1, 3, 5, 7 \right\}

B^{c} = \left\{2, 4, 5, 6 \right\}

Also:

A^{c} \cap B^{c}= \left\{5 \right\}

A \cup B=\left\{1, 2, 3, 4, 6, 7, 8 \right\}

\left(A \cup B \right)^{c}= \left\{ 5 \right\}, A \cap B= \left\{ 8 \right\}

\left(A \cap B \right)^{c}= \left\{ 1, 2, 3, 4, 5, 6, 7 \right\}

\left(A \cup B \right)^{c}= \left\{ 5, 8 \right\}

You’ve used 3 of your 10 free revision notes for the month

Sign up to get unlimited access to revision notes, quizzes, audio lessons and more

Sign up