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Grade 8 - Mathematics
4.2 Properties of Intersection

Commutative Property:
AB = BA
Example:
If A = {5,6,7,8,9} and B = {1,3,5,7,9}
AB = {5,7,9}
BA = {5,7,9}
Therefore, AB = BA.

Associative :
(AB)C = A (BC)
Example:
A = {1,2,3,4}, B = {4,5,6,7} and C = {2,4,6,8}
AB = {4}
(AB)C = {4}
BC = {4,6}
A(BC) = {4}
Therefore, (AB)C = A(BC)

Law of Identity:
A = A =
Example:
A = {1,2,3}
A = {1,2,3}{} =
A = {}{1,2,3}=
Therefore, A = A = .

Idempotent Law:
AA = A
Example:
A = {2,3,5,7}
AA = {2,3,5,7}{2,3,5,7}
= {2,3,5,7} = A
Therefore, AA = A

Intersection distributes over union:
A(BC) = (AB)(AC)
Example:
A = {1,2,3}, B = {3,4,5} and C = {3,5,7}
BC = {3,4,5}{3,5,7} = {3,4,5,7}
A(BC) = {1,2,3}{3,4,5,7} = {3}
AB = {1,2,3}{3,4,5} = {3}
AC = {1,2,3}{3,5,7} = {3}
(AB) (AC) = {3}{3}
Therefore, A(BC) = (AB)(AC).


Directions: Write at least five examples of your own for each property.

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