HELP - Venn Diagrams

Perhaps I just don't understand the question but it would be helpful if someone could give me some advice with this question.

You're not being asked to draw the standard Venn diagram for two sets each time.

You're being asked to choose an appropriate A and B, such that Z matches the criteria above. You need to choose how A and B related to each other.

As examples, one set could be the universal set, or they might not "overlap", etc.

Yes I know but they ask you to show the answers using a Venn diagram and since there's only A and B it's easiest just to show it using the standard Venn Diagram.

The question doesn't make sense to me. I've never experienced a question like this before. They give me a equation as to what Z is then expect me to illustrate what Z is on a Venn Diagram with these questions.

Yes, I see your point. If we consider a Venn diagram to contain all possible combinations of A,B then trying to demonstrate the various criteria, doesn't make sense.

Only if we relax the restriction of showing all possible combinations, and use Venn-like diagrams is it feasible, IMHO.

Perhaps someone else may have a useful comment, or check back with your lecturer, are the only things I can suggest.

...

'For any two non-empty sets A and B drawn from the same universe, U'

I'm guessing this means basically everything which isn't A or B is the universe U?

In each case you want to show Z.

So, yes for ii), I'd do two non-overlapping circles. In that situation, Z cannot equal B, as it contains A as well.



The universe will include A, and B. This is your outside oblong in the Venn diagram.

That's what I thought.

So for each case, you just label whatever part you think is Z.

I'm not sure what is the answer for (i), it's really confused me. How can you show that Z is an empty set? Unless you just show that there is no A or B and it's just the universe U?

Agreed.



Well you're told that A,B are non-empty, so you'll need a different solution.

Hint: If you break down Z into its two main components, what has to be true for each of them to be the empty set?

So both A and B are true instead of only 1 of them being true?

So for each case, you just label whatever part you think is Z.

A and B are sets, they're not "true". It's the relationship between them that has to exist for A\B to be the empty set. And similarly the other way around.

What if one of them was missing? Would it be an empty set? Or if it was B and C?

Really puzzled by this

Just consider A and B, neither of which is the empty set, but A\B is the empty set. What does this imply?

what does '\' mean?

Not yet, not sure if we cover that. We've got a lack of examples which is frustrating.

It doesn't tell you the set of elements that are in either sets?

So, there are no elements satisfying being "in A and not in B".

Ah A is a subset of B?

Bingo!!!!

So from the first part of the definition of Z you've worked out A is a subset of B.

Now what about the second part?