The wilson family invited 100 relatives to their christmas party. 90 guests had dutch heritage, 80 had german heritage and 75 had english heritage. what is the minimum number of people who claimed ancestry from all three heritages?

The minimum number of people would be 45. Let's try and separate it this way :
(100) Relatives = Rel | (90) Dutch = Dut | (80) German = Ger
100 Rel –> 90 Dut = 10 Rel and 90 RelDut
80 Ger –> 10 Rel = 10 RelGer | 70 Ger -> 70 Dut = 70 GerDut
So far we have 10 RelGer, 20 RelDut and 70 GerDut and 75 Eng.
Since we are trying to get the minimum number, we have to separate it again.
10 Ger -> 10 Eng = 10 GerEng | 20 Dut -> 20 Eng = 20 DutEng
Now you have 45 Eng left that will go to 45 GerDut = 45 GerDutEng, all three heritages.