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Union Intersection Relative Complement Absolute Complement Likened to Logical Or and Logical And Likened to logical Negation

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The union of two sets is the set that contains elements belonging to either of the two sets Equivalent to the Boolean operation “or” Written as: Examples: A = {a, b, c, d}B = {c, d, e, f} A B = {a, b, c, d, e, f} Note that the set could have been described as {a, b, c, d, c, d, e, f}

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A = {a, b, c, d} B = {c, d, e, f} A B = {a, b, c, d, e, f} A = {a, b, c, d} B = {x, y, z} A B = {a, b, c, d, x, y, z} Sets overlap Sets are disjoint

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The intersection of two sets is the set of all elements common to both sets The intersection of disjoint sets is the empty set Equivalent to the Boolean operation “and” written as: Examples: A = {a, b, c, d} B = {a, b}B = {x, y, z} A B = {a, b}A B =

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A = {a, b, c, d} B = {a, b} A B = {a, b} A = {a, b, c, d} B = {x, y, z} A B =

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The relative complement (difference) of two sets is the set of elements contained in one, but not both, of the sets Related to the Boolean “Exclusive Or” Written as: — Examples: Given: A = {a, b, c, d} and B = {a, c, f, g} A — B = {b, d} B — A = {f, g}

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A = {a, b, c, d} B = {a, c, f, g } A — B = {b, d} B — A = {f, g}

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The absolute complement of a set is the set of elements which do not belong to the set being complemented’ Equivalent to the Boolean operation “not” Written as a superscripted ‘c’ Example: U = {a, b, c, d, e, u, v, w, x, y, z} A = {a, b, c, x, y, z} and B = {a, b, c, d, e} A c = {d, e, u, v, w} B c = {u, v, w, x, y, z}

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U = {a, b, c, d, e, u, v, w, x, y, z} A = {a, b, c, x, y, z} B = {d, e, y, z} A c = {d, e, u, v, w}

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Illustrates the 8 possible relations be- tween Sets, A, B and C

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Shows whether an arbitrary element x be- longs in any of the indicated sets.

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Idempotent Laws A A = A A A = A Associative Laws (A B) C = A (B C) (A B) C = A (B C) Commutative Laws A B = B A A B = B A

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Distributive Laws A (B C) = (A B) (A C) A (B C) = (A B) (A C) Identity Laws A = A A U = U A U = A A =

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Complement Laws A A c = U U c = A A c = c = U De Morgan’s Laws (A B) c = A c B c (A B) c = A c B c

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