Venn Diagrams: Describing set relations from diagrams

[Timcago]

For the following Venn Diagrams, describe the shaded set using unions and intersections of events A, B, Non A, and Non B

For the first one my guess was: B - (A and B)

for the second my guess is: Non A + Non B + (A and B)

Are my answers correct?

 

[tkhunny]

Why are you "guess"ing? It appears to me that subtraction is not in the problem statement as a valid method.

a) How about [B and (not A)]

b) No good. You have included the middle section that is not shaded. Again, though, with the addition. Who said you could do that? Perhaps [not (A or B)] which is equivalent to [(not A) and (not B)]

Do another one and show us what you get.

 

[Timcago]

I am getting a little confused because different stats teachers use different symbols.

(A or B) = (A U B)
(A and B) = (A [upsidedown U] B)
by Not A its referring to a complementary event

The way you are doing it looks to be the appropriate method. I thought that adding numbers that are solo to stuff looked funny.

However, on part b, when you do [(not A) and (not B)], you are only taking away the intersection of A and B. Everything in both A and B need to be taken away not just the values in their intersection.

If you were to do [(not A) or (not b)] you are taking away all elements in set A and taking away all elements in set B, but since events A and B intersect you are taking away what is shared by Both A and B 2 times. That is why I added and extra (A and B).

EDIT: Now that i think about it if you are taking away all the elements in the intersection twice, you still have the same result as taking away all the elements 1 time, which is no values, so i guess you were right?

 

[Timcago]

Here are my new answers

A) (B U Ā)

^ I am assuming that in words that says: All elements of set B with No elements of set A including none of the elements that A and B share.

B) [(Ā) U (not b)]

^ in words that says take away all elements in set A, take away all elements in set B.

 

[pka]

The Venn diagram in (b) is for: \(\displaystyle \overline {\left( {A \cup B} \right)}.\)
That is: Not(A or B).