Distributive Laws for sets

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October 12th 2009, 04:12 PM
minkyboodle

Distributive Laws for sets

One of the following distributive laws for sets is true. Which one is and what is the proof?

A $\cap$ (B $\oplus$ C)=(A $\cap$ B) $\oplus$ (A $\cap$ C)

A $\cup$ (B $\oplus$ C)=(A $\cup$ B) $\oplus$ (A $\cup$ C)
October 12th 2009, 04:55 PM
Plato

I think all you need to notice is that
$B \oplus C = \left( {B \cap C^c } \right) \cup \left( {B^c \cap C} \right)$
October 12th 2009, 05:01 PM
minkyboodle

so, which one is right?
October 12th 2009, 05:22 PM
Plato

Quote:

Originally Posted by minkyboodle

so, which one is right?

That is for you to work out.
Why do you expect to be handed the answer?
Is this not a question given to you after all?
October 12th 2009, 06:47 PM
HallsofIvy

This makes 6 homework problems you have posted without any sign of an attempt to do the problems yourself. You can't learn by having other people do your work for you!

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