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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

Grade 8 - Mathematics
4.45 Ac Bc =(AB)c

EXample:
If U = {1,2,3,4,5,6,7,8,9}, A = {1,2,3,4,5} and B = {1,3,5},
then prove that Ac Bc = (A B)c.

Solution:
Ac = U - A = {1,2,3,4,5,6,7,8,9} - {1,2,3,4,5}
= {6,7,8,9}
Bc = U - B = {1,2,3,4,5,6,7,8,9} - {1,3,5}
= {2,4,6,7,8,9}
Ac Bc = {6,7,8,9} {2,4,6,7,8,9}
= {2,4,6,7,8,9}
A B = {1,2,3,4,5} {1,3,5}
= {1,3,5}
(A B)c = U - (A B) = {1,2,3,4,5,6,7,8,9} - {1,3,5}
= {2,4,6,7,8,9}
Therefor, Ac Bc = (A B)c.


Directions: Write at least five examples of your own and prove that Ac Bc = (A B)c

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

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