1.5 Set Operations with Three Sets

Three overlapping circles: reading and building the eight regions, chaining operations across them, and proving two expressions equal by shading.

Contemporary Mathematics, 1.5 Set Operations with Three Sets

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1.5 Exercise 5

Perform the set operations as indicated on the following sets: $U = \left\{0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12\right\}$ , $A = \left\{0 , 1 , 2 , 3 , 4 , 5 , 6\right\} ,$ $B = \left\{0 , 2 , 4 , 6 , 8 , 10 , 12\right\} ,$ and $C = \left\{0 , 3 , 6 , 9 , 12\right\} .$

Find $\left(A \cap B\right) \cap C .$
Find $A \cap \left(B \cup C\right) .$
Find $\left(A \cap B\right) \cup C^{'} .$

2.5