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I was doing the following question.

    illustrate the following using a venn diagram 
    A – B =  ~(~A ∪ B)     where as usual A-B={x : x ∈ A & x ∉ B}

I got the following.

i got the following

But surely A-B should look like this?

enter image description here

I'm really unsure about the steps I have to take to get to each step.

Could someone explain please?

Thanks!

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  • $\begingroup$ Why should $A-B$ not have elements from $A$ that are not in $B$? $\endgroup$ – user21436 May 1 '12 at 9:57
  • $\begingroup$ Oops i think im getting confused between A-b and ~A and ~B $\endgroup$ – Xabi May 1 '12 at 9:59
  • $\begingroup$ Fine, so, do you get that the second diagram is not right? $\endgroup$ – user21436 May 1 '12 at 10:01
  • $\begingroup$ Yes, does that mean the first one is right? $\endgroup$ – Xabi May 1 '12 at 10:01
  • $\begingroup$ Yes, sure it does. What you have first is right one for $A-B$ and the second diagram is the right one for $\lnot A \cap \lnot B$ which is also $(A \cup B)^c$ y DeMorgan's laws. $\endgroup$ – user21436 May 1 '12 at 10:07
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It should be like this :

enter image description here

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  • $\begingroup$ yes exacly @pedja ,as i indicated in my comment +1 $\endgroup$ – dato datuashvili May 1 '12 at 10:15

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