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It's essential that we understand the set equation:

n(A u B) = n(A) + n(B)- n(A n B), wfromhere U=Union and n= intersection of sets, respectively.

We've n(A)=50 and n(B)=60. So, n(A U B)= 110- n( A n B).

Total no of patients with heart disease=100.

Then, n(A n B)<= 100. It follows that -n(A n B)>= -100, or, 110 -n(A n B)>= 10, or, n(A U B)>= 10.

Also n(A U B)<= 100.

Combining them we've,

10>= n(A U B)<= 100. Thus, the total no. of patients having disease A or B or both vary from 10% to100%.

Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

Over 15 years teaching at the college level.**Organizations belong to**

NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.**Education/Credentials**

B.S. in Mathematics from Rensselaer Polytechnic Institute

M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook