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Grade 8 - Mathematics
4.7 Properties of Union

Commutative Property :
A B = B A.

Example:
If A = {1,2} and B = {3,4}
A B = {1,2} {3,4}.
= {1,2,3,4}.
B A = {3,4} {1,2}.
= {1,2,3,4}.
\ A B = B A.

Associative Property:
(A B) C = A (B C).

Example:
If A = {a,b}; B = {c,d} and C = {e,f}
(A B) C
A B = {a,b} {c,d}
= {a,b,c,d}
(A B) C= {a,b,c,d} {e,f}.
{a,b,c,d,e,f}.
A (B C)
B C = {c,d} {e,f}.
= {c,d,e,f}.
A (B C) = {a,b} {c,d,e,f}.
{a,b,c,d,e,f}.
\ (A B) C = A (B C)

Law of Identity:
A = A

Example:
If A = {2,3,4} and = {}
A = {2,3,4} {}
{2,3,4}
A = {} {2,3,4}
{2,3,4}
\ A = A.
\ is the identity set for the operation of the Union.

Idempotent Law:
A A = A

Example:
A = {a,b,c}
A A = {a,b,c} {a,b,c}
{a,b,c}
A.
\ A A = A.


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

Have your essay responses graded by your teacher and enter your score here!

Your score for this chapter (0-100%) =


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