Problema Solution
You are given merchant data to perform an analysis of credit cards accepted at merchant locations. There are 134 merchants in the data-set, 86 merchants accept Visa, 91 accept M/C, and 83 accept AMEX. 25 merchants accept Visa & M/C, but not AMEX; 17 accept Visa & AMEX, but not M/C; 37 that accept Visa, M/C & AMEX. How many merchants accept AMEX & M/C, but not Visa?
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Answer provided by our tutors
Draw Venn's diagram with 3 sets:
V = sets of Visa owners
M = set of M/C owners
A = set of AMEX owners.
such that
(intersection of V and M) \ A has 25 elements
(intersection of V and A) \ M has 17 elements
intersection of V, A and M has 37 elements
let x be the number of elements in (intersection of A and M) \ V thus we can write
the number of elements in A U V U M is
|A U V U M| = 86 + 91 + 83 - (17 + 25 + 2*37 + x) = 144 - x
There are 134 merchants in the data-set
|A U V U M| = 134
144 - x = 134
x = 10
10 merchants accept AMEX & M/C, but not Visa.