UNH Universal Quantifier Set Math Worksheet

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Problem 5. (20 points] Given a finite set A, we denote its size (number of elements) as |A]. The
Jaccard similarity J(A, B) of the finite sets A and B is defined to be J(A, B) = |An B/|AU BI,
with J(0,0) = 1. The Jaccard distance dj(A, B) between A and B equals dj(A,B) = 1- J(A,B).
a) Find J(A, B) and dj(A.B) for these pairs of sets:
1. A = {1,3,5}, B = {1, 2, 4, 6}
2. A=0, B = {0}
b) Prove that J(A,B) = 1 if and only if A = B.

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