Complement Of A Set

The complement of set A, denoted by A’ , is the set of all elements in the universal set that are not in A.

The number of elements of A and the number of elements of A ’ make up the total number of elements in U .

n(A) + n(A ’ ) = n( U )

Example:

Let U = {x : x is an integer, –4 ≤ x ≤ 7}, P = {–4, –2, 0, 2, 4, 5, 6} and

Q ’ = {–3, –2, –1, 2, 3}.

a) List the elements of set P ’

b) Draw a Venn diagram to display the sets U , P and P ’

c) Find n(Q)

Solution:

a) First, list out the members of U.

U = {–4, –3, –2, –1, 0, 1, 2, 3, 4, 5, 6, 7}

P ’ = {–3, –1, 1, 3, 7} ← in U but not in P

b) Draw a Venn diagram to display the sets U , P and P ’

c) Find n(Q)

n( U ) = 12, n(Q ’ ) = 5

Use the formula:

n(Q) + n(Q ’ ) = n( U )

n(Q) = n( U ) – n(Q ’ ) = 12 – 5 = 7

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