Venn diagrams

What is ( A C ) ? (A \cap C)'?

{ 3 , 4 , 6 , 7 , 9 , 10 } \{3,4,6, 7,9,10\} { 5 , 8 } \{5,8\} { 5 , 4 } \{5,4\} { 3 , 4 , 5 , 6 , 7 , 8 } \{3,4,5, 6, 7,8\}

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2 solutions

Munem Shahriar
Sep 2, 2017

From the venn diagram,

U = { 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 } U = \{3,4,5,6,7,8,9,10\}

A = { 3 , 4 , 5 , 8 } A = \{3,4,5,8\}

C = { 5 , 6 , 7 , 8 } C = \{5,6,7,8\}

( A C ) (A \cap C)'

= U { 3 , 4 , 5 , 8 } { 5 , 6 , 7 , 8 } = U - \{3,4,5,8\} \cap \{5,6,7,8\}

= { 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 } { 5 , 8 } = \{3,4,5,6,7,8,9,10\} - \{5,8\}

= { 3 , 4 , 6 , 7 , 9 , 10 } = \{3,4,6,7,9,10\}

( A C ) = U ( A C ) (A \cap C)' = U - (A \cap C) .

5 5 and 8 8 are the elements of ( A C ) (A \cap C) .

So, the option without 5 5 and 8 8 is the answer.

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