Chapter_05-4up

# Chapter_05-4up - Show A \$ B and B \$ A John Hannan Comp Sci...

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Comp Sci 360 - Fall 2009 Set Theory Membership, Subset, Equality Universal Set U, Empty Set ! Union, Intersection, Difference, Complement Disjoint Sets, Partitions Power Sets, Products John Hannan - Comp Sci 360 - Fall 2009 Sets Subset Transitivity Commutivity Associativity Distributivity John Hannan - Comp Sci 360 - Fall 2009 Properties of Sets John Hannan - Comp Sci 360 - Fall 2009 Additional Properties (1)A "! =A A # U=A (2)A " A c = U A # A c = ! (3)(A c ) c = A (4)A " A=A A # A=A (5)A " U=U A #! = ! (6)(A " B) c = A c # B c (A # B) c = A c " B c (7)A " (A # B)=A A # (A " B) = A (8)U c = ! ! c = U (9)A-B = A # B c

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John Hannan - Comp Sci 360 - Fall 2009 Proving Properties To prove A \$ B: Assume x % A; Show x % B To prove A=B:
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Unformatted text preview: Show A \$ B and B \$ A John Hannan - Comp Sci 360 - Fall 2009 Boolean Algebra (1) Set B (2) Two operations + and & Associative, Commutative, Distributive (3) Two distinct elements 0 and 1 in B such that a+0 =a and a & 1=a for all a % B (4) Complement of every element exists John Hannan - Comp Sci 360 - Fall 2009 Properties (1) if a+x=1 and a & x=0 then x = a (2) 0 and 1 are unique (3) (a) = a (4) a+a=a and a & a=a (5) a+1 =1 and a & 0 = 0 (6) a+b = a & b and a & b = a + b (7)(a+b) & a = a and (a & b)+a = a (8) 0 = 1 and 1 = 0...
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## This note was uploaded on 10/04/2009 for the course CMPSC 360 taught by Professor Haullgren during the Fall '08 term at Penn State.

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Chapter_05-4up - Show A \$ B and B \$ A John Hannan Comp Sci...

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