union and difference

set theory.

So if this union

B U C = C;

equals

B \ C = 0 ( 0 is empty set )

how can I show that?

second part like this;

B \ C = 0 so B:= {1,2,3} and C:= {1,2,3} Thus B \ C = 0 ( 0 is empty set)
? and the first part?

What do you mean by "showing" the given relations? Are the equations not sufficient, in and of themselves, for some reason? :?:

Hi. Sorry. I just want to show that those following two terms are congruent with each other.

What "terms"? You posted two equations...?

It might help if you posted the full and exact text of the exercise, along with the complete instructions, so we can see what is being asked of you. Thank you! :wink:

Thank you. Okay.


show, that, following criterias/terms are congruent with each other.

B U C = C;

B \ C = Ø ( Ø is empty set, not 0 )

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and here's how I tried;


So if this union

B U C = C;

equals

B \ C = Ø ( Ø is empty set )

how can I show that?

second part like this;

B \ C = Ø so B:= {1,2,3} and C:= {1,2,3} Thus B \ C = Ø (Ø is empty set)
? and the first part?

I don't know what you mean by "the second part", since none appears to be included in the exercise...?

To show set equality, use the standard method of "element chasing". For instance, pick an element e from B U C, noting that B U C = C. Then e is in C. But e might also be in B. Suppose so. Now look at B \ C. If e is in B and not in C, then e is in B \ C. But if e is in B and not in C, then B U C cannot equal C; at best, it will equal C U {e}. So what can you conclude?

And work similarly in the other direction. :wink:

Thanks!

AND: And if e is in B AND e is in C. And if we take a look at B \ C. It will now be B \ C = 0 ( 0 means an empy set ), because e is in B and in C, and
e disappears as a result of this difference.

Is it now finished?