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

## Presentation on theme: " Union  Intersection  Relative Complement  Absolute Complement Likened to Logical Or and Logical And Likened to logical Negation."— Presentation transcript:

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

 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}

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

 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 = 

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

 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}

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

 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}

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}

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

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

 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

 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   = 

 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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