SOLUTION: Suppose that A, B, and C are all subsets of the universal set U. First construct a Venn Diagram for . Now answer the following question. Which of the following would

None of those turn out to have the same Venn diagram.
I'll go through them to show what regions are to be shaded in each:



The sets are denoted by capital letters A,B, C

The disjoint regions that make them up are denoted with small letters.

Since I can't shade anything on here,  I will use the convenient although 
non-standard notation that when small letters are written side by side it 
means the union of those regions.

So A = degh,  B= efhi, C= ghij

A' ∪ (B ∩ C)

degh' ∪  (efhi ∩ ghij)

Do the parentheses first. ∩ means to take only the regions in common,
so the parentheses becomes hi

degh' ∪  hi

degh' means to take all the regions in the entire Venn diagram 
EXCEPT degh, which means fijk, so the above becomes:

fijk ∪  hi

The ∪  means to take all the regions that are on either side of the ∪ 

So the answer is this union of regions:

fhijk

So you would draw a Venn diagram and shade regions f,i,j,k,g, and h

----------------------------------------------
A ∩ (B' ∪ C')

degh ∩ (efhi' ∪ ghij')

efhi' means to take all the regions in the entire Venn diagram 
EXCEPT efhi, which means dgjk, so the above becomes:

degh ∩ (dgjk ∪ ghij')

ghij' means to take all the regions in the entire Venn diagram 
EXCEPT ghij, which means defk, so the above becomes:

degh ∩ (dgjk ∪ defk)

The ∪  means to take all the regions that are on either side of the ∪,
so the parentheses becomes defgjk, and we have:

degh ∩ defgjk

∩ means to take only the regions in common, so we get this:

deg

So you would draw a Venn diagram and shade regions d,e, and g

-----------------------------------

A ∩ B ∩ C

degh ∩ efhi ∩ ghij

Since ∩ means to take only the regions in common, h is the only
region in common, so this becomes only 

h
So you would draw a Venn diagram and shade only the middle region h

----------------------------------

A ∩ B' ∩ C'

degh ∩ efhi' ∩ ghij'

The apostrophes are "complements" which means to take all the regions 
in the entire Venn diagram EXCEPT the ones before the ', so the above
becomes:

degh ∩ dgjk ∩ defk

∩ means to take only the regions in common, so that becomes only d

d

So you would draw a Venn diagram and shade only the upper left region d

Edwin