Discrete Mathematical Structures
Discrete Mathematical Structures CSCI 2427
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This 3 page Study Guide was uploaded by Else Dooley on Sunday October 11, 2015. The Study Guide belongs to CSCI 2427 at East Carolina University taught by Robert Hochberg in Fall. Since its upload, it has received 71 views. For similar materials see /class/221319/csci-2427-east-carolina-university in ComputerScienence at East Carolina University.
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Date Created: 10/11/15
Discrete Math Class 21March 6 2004 At the being of class we took at quiz and then discussed about some different types of sets Empty Set Definition the set with no elements Therom VA A A is a set Proof Vxx gtx A True Statement x U don t know were A is o A propostion of the form Vx PX gtQx is called vacuously satisfied or vacuously true if Px is false for all values of x Power Set Definition ifA is a set then the power set of A denoted 2A or PA is the set of all subsets of A note you can take the power set of only a set and it will give you another set Set Power of Operation Set Example A15 PA1515 the sets are subsets of A Example find Pabc F abc abcabacbcabc Example taking the power set of a power set PP7 PP7P 7 Q Q7 7 0 Note that 7 is not the same as 7 gt This set has 1 element namely 7 gt This set has 1 element namely 7 0 Sometimes it is helpful to list a sets elements explicitly when answering an apparently tricky question gt Example is 23 232 Elements of 23 are 2 and 3 Elements of 232 are 23 and 2 It is not a subset because the elements on the left side are not on the right side of the equation Important Fact about Sets the elements in a set have no intrinsic order Thus 1 551 5432115243 Cardinality Definition let A be a set and A means the size of A and is the number of elements of A Example 234 3 Example 0 Example 2344324 Example A5100 says A has at most 100 elements Fact PA 239 Cartesian Product of Sets Definition lf A1 A2 AK are sets then A1 xA2x xAK is the set of ordered Ktuples a1 a2 a3 ak where a1 A1 a2 A2 ak Ak IR X IR IR xyx lR y lR Example A23 BJohnSallyBill A x B2John2Say2Bill3John3Sally3Billy Matter how you write the pairs gt Example 2John is not the same as John2
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