Misalkan : S
= {x │ x bilangan bulat positif, x ≤ 10}
P
= {1, 2, 3, 7}
Q
= {2, 4, 6, 9}
R
= {1, 3, 5, 8}
(P U Q) ∩ (P’ ∩ R)’ = P U (Q’ U R)’
P U Q = {1, 2, 3, 7} U
{2, 4, 6, 9}
= {1, 2, 3, 4,
6, 7, 9}
P’ = {4, 5, 6, 8,
9, 10}
P’ ∩ R = {4, 5, 6, 8,
9, 10} ∩ {1, 3, 5, 8}
= {5, 8}
(P’ ∩ R)’ =
{1, 2, 3, 4, 6, 7, 9, 10}
(P U Q) ∩ (P’ ∩ R)’ = {1, 2, 3, 4, 6, 7, 9} ∩ {1, 2, 3,
4, 6, 7, 9, 10}
=
{1, 2, 3, 4, 6, 7, 9}
Q’ = {1, 3, 5, 7,
8, 10}
Q’ U R = {1, 3, 5, 7,
8, 10} U {1, 3, 5, 8}
= {1, 3, 5, 7,
8, 10}
(Q’ U R)’ =
{2, 4, 6, 9}
P U (Q’ U R) = {1, 2, 3, 7} U {2, 4, 6, 9}
=
{1, 2, 3, 4, 6, 7, 9}
(P U Q) ∩ (P’ ∩ R)’ = P U (Q’ U R)
{1, 2, 3, 4, 6, 7, 9} = {1, 2, 3, 4, 6, 7, 9}
Jadi terbukti sama.
