Question

# Set theory proof: Rearrange: (A U B) X (C U D) to equal (A X C)...

Set theory proof:

Rearrange: (A U B) X (C U D) to equal (A X C) U (B X D)

I get stuck after the following steps:

1. (x,y) exist (A U B) X (C U D)

2. x exist (A U B) X y exist (C U D)

3. (x exist A OR x exist B) AND (y exist C OR y exist D)

I know that somehow we can get to but I need it explained:

4. (x exist A AND y exist C) OR (x exist B AND y exist D)

I need a full explanation of how we can get from step 3 to 4.

#### Homework Answers

Answer #1

x ∈ A means x belongs to A

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