For all sets A, B, and C, we have the identity Ax (B-C) = (A x B)-(A x C). . Use element chasing to prove this identity. Using the identities from Section 5.4 would make the statement trivial to show. . Consider reading the proofs of Proposition 5.11 and Theorem 5.25 in the text to see examples of proof by element chasing . As always with set equality proofs, prove that the lefthand side of the equality is a subset of the righthand side and vice versa. . Keep in mind that the sets described here are Cartesian products, so their elements are ordered pairs. You would start with something like "Let (z,y) E Ax (B-C):" rather than "Let z EA x (B-C):.

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