For sets A, B, and C, prove that A - (B C) = (A - B) U (A - C).?

Note that a partition of a set S has subsets of S as members. These members/subsets follow some restrictions. A member of a partition of S is actually a subset of S. Let P1 denote a partition of set S = {1, 2, 3, 4} such that it has 3 members. For example P1 = { {1, 2}, {3}, {4} } could be one such partition.

For sets A, B, and C, prove that A - (B C) = (A - B) U (A - C).?
x (is a member of) A - (B U C).


x (is a member of) A (and) [(not) (B (or) C)]


x (is a member of) A (and) [ (not) B and (not) C]


x (is a member of) [A (and) (not) B] (or) x (is a member of) [A (and) (not) C]


x (is a member of) ([A - B] (or) [A - C])


[A-B] U [A-C]





QED

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