Show that the set difference metric given by d(A, B) = size(A B) + size(B A) satisfies the metric axioms given on page 70. A

Show that the set difference metric given by
d(A, B) = size(A ˆ’ B) + size(B ˆ’ A)
satisfies the metric axioms given on page 70. A and B are sets and A ˆ’ B is the set difference.

1.4 1.4 1.2 0.8 0.6 0.4 0.2 0.8 0.4 0.2 0.2 0.4 0.6 0.8 Cosine Similarity 0.2 0.4 0.6 0.8 Correlation (a) Relationship between Euclide distance and the cosine measure (b) Relationship between Euclidean distance and correlation