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### Grade 8 - Mathematics4.2 Properties of Intersection

 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.