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# Set Theory: Set Operations

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Bridge to Abstract Mathematics
Set Theory: Set Operations

Let A, B, C and D be sets. Prove that....
a) A B iff A B = Ø.
b) If A B U C and A ∩ B = Ø, then A C.
c) C A ∩ B iff C A and C B.
d) If A B, then A C B C.
e) (A B) C = (A C) (B C).
f) If A C and B C, then A U B C.
g) (A U B ) ∩ C A U (B ∩ C).
h) A B and B are disjoint.
i) If C A and D B, then C ∩ D A ∩ B.
j) If C A and D B, then C U D A U B.
k) If C A, D B, and A and B are disjoint, then C and D are disjoint.
l) If C A and D B, then D A B C.
m) If A U B C U D, A ∩ B = Ø, and C A, then B D.

https://brainmass.com/math/discrete-math/set-theory-set-operations-348757

#### Solution Preview

Proof:
a) If , then , thus .
If , then , thus .
b) If , and , then , thus .
c) If , then and , then and ; if and , then , thus .
d) If , then ...

#### Solution Summary

Provide an example of each type of proof attached.

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