Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

i am trying to prove this statement, it is obvious, but i just cannot get the clue where and how to start to prove that this statement is true.

the statement is this: $(A \setminus C)\times(B \setminus D)\subset(A \times B)\setminus(C \times D)$

i am starting like this:

$x \in A \wedge x \notin C \times x \in B \wedge x \notin D $ ... but i dont know how to come to the idea that this is a subset of the right side of the first statement. :(

can someone give me a hint please?

thanks a lot

share|improve this question

2 Answers 2

up vote 6 down vote accepted

Pick an element in the left side, and show its in the right side.

Suppose $(x,y)\in (A\setminus C) \times (B\setminus D)$.

Then we have that $x\in A$, $x\notin C$ and $y\in B$, $y\notin D$.

So since $x\in A$ and $y\in B$ what can we say about $(x,y)$?

And since $x\notin C$ (and $y\notin D$) what can we say about $(x,y)$?

share|improve this answer
1  
+1 Very nicely done. –  amWhy Nov 11 '12 at 18:48
    
wow, thanks, i got the $ clue $ :) –  doniyor Nov 11 '12 at 18:51
    
@doniyor glad I could help! –  Deven Ware Nov 11 '12 at 19:02

Actually, your starting point is false. You have to start with the definition of "Cartesian product ". So, $(x,y) \in (A-B)\times (B-D)$ must be your start point. Then, your next step will be: $x \in (A-B) \wedge y\in(B-D) $.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.