Commutative Property:
AÇB = BÇA
Example:
If A = {5,6,7,8,9} and B = {1,3,5,7,9}
AÇB = {5,7,9}
BÇA = {5,7,9}
Therefore, AÇB = BÇA.
Associative :
(AÇB)ÇC = A Ç(BÇC)
Example:
A = {1,2,3,4}, B = {4,5,6,7} and C = {2,4,6,8}
AÇB = {4}
(AÇB)ÇC = {4}
BÇC = {4,6}
AÇ(BÇC) = {4}
Therefore, (AÇB)ÇC = AÇ(BÇC)
Law of Identity:
AÇÆ = ÆÇA = Æ
Example:
A = {1,2,3}
AÇÆ = {1,2,3}Ç{} = Æ
ÆÇA = {}Ç{1,2,3}= Æ
Therefore, AÇÆ = ÆÇA = Æ.
Idempotent Law:
AÇA = A
Example:
A = {2,3,5,7}
AÇA = {2,3,5,7}Ç{2,3,5,7}
= {2,3,5,7} = A
Therefore, AÇA = A
Intersection distributes over union:
AÇ(BÈC) = (AÇB)È(AÇC)
Example:
A = {1,2,3}, B = {3,4,5} and C = {3,5,7}
BÈC = {3,4,5}È{3,5,7} = {3,4,5,7}
AÇ(BÈC) = {1,2,3}Ç{3,4,5,7} = {3}
AÇB = {1,2,3}Ç{3,4,5} = {3}
AÇC = {1,2,3}Ç{3,5,7} = {3}
(AÇB) È(AÇC)
= {3}Ç{3}
Therefore, AÇ(BÈC) = (AÇB)È(AÇC).
Directions: Write at least five examples of your own for each property.
