Thread: Logic symbol question

I am asked to draw a venn diagram of a few sets. But next to them there is a small C and I have no clue what that small C means.

To see it in context look at question 6 here. Thanks so much for any help!!!

CS2130 Assignment 1

In this context is the relative complement.
That is

so..

6. Make a Venn diagram illustrating the case

Ac∩Bc∩C = Ac∩B∩Cc = ∅, B ≠ C, and B ∩ C ≠ ∅.

Few questions...

This is supposed to be one single venn diagram.

This is asking me to show that...
A compliment intersect B compliment intersect C = A compliment intersect B intersect C compliment=null set?

So is also says that B does not intersect C. So if B does not intersect C and I show Ac∩Bc∩C I end up with the area of C shading in that does not intersect A, which does not equal the null set.

Ac∩B∩Cc for this I get the area of B shaded in that does not intersect A.


Here is how I got it those two.

First this means B ∩ C ≠ ∅ that B and C do not intersect.

So my venn is circle B intersecting circle A which intersects circle C.

So A compliment is everything outside of A.

B compliment is everything outside of B

Ac intersect Bc is everything outside of A and B

and Ac intersect Bc intersect C is everywhere that is both outside of A and B and in C which ends up being the area of C not intersect by A. So I am confused at how this can = the null set.

Here is the Venn diagram of

Yes that is what I got!!! So how can that possibly =∅?????? I am confused!

Originally Posted by ehpoc

Yes that is what I got!!! So how can that possibly =∅?????? I am confused!

Well now do the same for .
Do you see any overlapping?

Ya but the question asked to show..

Ac∩Bc∩C = Ac∩B∩Cc = ∅

Not

(Ac∩Bc∩C) ∩ Ac∩B∩Cc = ∅

unless does that "=" in the middle mean intersection???

Originally Posted by ehpoc

Ya but the question asked to show..



Not



unless does that "=" in the middle mean intersection???

But you are also given that

But you are also given that B\cap C=\emptyset

Which I thought meant that B and C do not intersect anywhere.

So Ac∩Bc∩C is...





and Ac∩B∩Cc is..




Neither of these diagrams are equal and neither = \emptyset