Is the Distributive Property Applicable in this Set Theory Problem?

[nicnicman]

Hello all, while practicing set theory, I cam across this problem:

If A and B are sets, prove that A x (B-C) = (AxB) - (BxC).

This looks suspiciously like the distributive property but it's not. Is this simply a typo? Shouldn't the problem look like this:

A x (B-C) = (AxB) - (AxC)

Thanks for any suggestions.

 

[Bonaparte]

You can easily check and understand its a typo.
Let A = {1,2},
B = {3,4}
C = {3}.
AX(B-C) = (1,4) (2,4)
AXB 1,4 2,4 1,3 2,3, and BXC = 3,3 4,3.
I hope I'm not making a full of myself and your doing things that are much more complicated then what I just said :)

Thanks, Bonaparte

 

[nicnicman]

No, you're not making a fool of yourself. I think it's a typo too.