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