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I have to find an example illustrating the the equation
(A x B) U (X x Y) = (A U X) x (B U Y) is not valid for all choices of sets A,B,X,Y.
I started out by saying that
let (x,y) be in A and B or
let (x,y) be in X and Y
Since x is in A and y is in B
--> (x,y) = (A x B)
Since x is in X and y is in Y
--> (x,y) = (X x Y)
Can I go on to say that since x is in A and x is in A
x is a subset of (A U X)?
How do I prove that this is not true?
(A x B) U (X x Y) = (A U X) x (B U Y) is not valid for all choices of sets A,B,X,Y.
I started out by saying that
let (x,y) be in A and B or
let (x,y) be in X and Y
Since x is in A and y is in B
--> (x,y) = (A x B)
Since x is in X and y is in Y
--> (x,y) = (X x Y)
Can I go on to say that since x is in A and x is in A
x is a subset of (A U X)?
How do I prove that this is not true?