Question

HELP! for arbitrary sets A, B, C, and D. (AxB)U(CxD)=(AUC)x(BUD). True or false? Prove your answer.

Answer 1

what do you think?

Answer 2

False? I really am not good at understanding sets and set theory

Answer 3

what would you get if A and D were empty sets?

Answer 4

BUC?

Answer 5

=CXB

Answer 6

if \(A=D=\emptyset\)

then

\(A\times B=\emptyset\) and \(C\times D=\emptyset\)

and therefore \((A\times B)\cup(C\times D)=\emptyset\)

Answer 7

\(A=D=\emptyset\)

then

\(A\cup C=C\) and \(B\cup D=B\)

thus \((A\cup C)\times(B\cup D)=C\times B\)

Answer 8

ok?

Answer 9

okay but they are arbitrary set

Answer 10

which means we don't know if they are empty or not

Answer 11

I just gave you a blueprint on how to construct a counter example