# Shared Flashcard Set

## Details

CIS 1910 Exam
A List of things that may appear on he exam
77
Computer Science
04/08/2010

Term
 Let U and V Be two sets.  A binary relation over U and V is a triple R = (U,V,G).   What are the domains of the R?
Definition
 The domains of R is U and V
Term
 Let U and V Be two sets.  A binary relation over U and V is a triple R = (U,V,G).   What is G a subset of?
Definition
 G is a subset of UxV
Term
 Let U and V Be two sets.  A binary relation over U and V is a triple R = (U,V,G).   What represents the Graph of R?
Definition
 G is the Graph of R
Term
 Let U and V Be two sets.  A binary relation over U and V is a triple R = (U,V,G).   How Can uRv be rewritten? (Read " U is related to v by R")
Definition
 (u,v) [image]  G
Term
 let U, V, and W be a Quadruple (U,V,W,G) Where G is a Subset of UxVxW.   What type of  relation ship does this form with respect to R?
Definition
 It is a ternary relation R over U,V, W.
Term
 let U, V, and W be a Quadruple (U,V,W,G) Where G is a Subset of UxVxW. What is the Domain of R?
Definition
 U, V, W are the domains of R
Term
 let U, V, and W be a Quadruple (U,V,W,G) Where G is a Subset of UxVxW. What is the graph of R?
Definition
 G represents the Graph of R
Term
 let U, and  Vbe a Binnary relation R =(U,V,G) ?   What is the Inverse of R
Definition
 R-1 = (V, U, G-1) With G-1 = {(v,u) [image] VxU | uRv}
Term
 Consider Two Binary relations R1= ( U, V, G1) and R2 = (V,W,G2) What is the composite of R1 and R2?
Definition
 The Composite of R1 and R2 is R2 º R1 = (U,W,G) With G = {(u,w) [image] UxW |[image]v [image]V,(uR1 V  vR2w)}
Term
 Consider Two Binary relations R1= ( U, V, G1) and R2 = (V,W,G2) What is R1  [image] R2?
Definition
 R1  [image] R2 = (U, V,G1  [image]  G2)
Term
 Let R be a binary relation on some set U What is an example of Reflexove iff:
Definition
 [image] u (uRu)
Term
 Let R be a binary relation on some set U What is an example of Symmetric iff:
Definition
 [image] u  [image]  v (uRv → vRu)
Term
 Using the following graph adjustx to show reflexive closure? [image]
Definition
 you only have to change the two highlighted in Orange [image]
Term
 Using the following graph adjustx to show symmetric closure? [image]
Definition
 you only have to change the two highlighted in Orange  [image]
Term
 Using the following graph adjusts to show transitive closure? [image]
Definition
Term
 What type of gate is this [image]
Definition
 An And Gate
Term
 What type of gate is this [image]
Definition
 The gate is a is Gate
Term
 What type of gate is this [image]
Definition
 It is an Or Gate
Term
 Solve this Circuit[image]
Definition
 [image]
Term
 This is a Nor Gate and is defined by the following[image] Use Just Nor gate to form an [image]
Definition
 [image]
Term
 This is a Nor Gate and is defined by the following[image] Use Just Nor gate to form an X+Y
Definition
 [image]
Term
 This is a Nor Gate and is defined by the following[image] Use Just Nor gate to form an X[image]Y
Definition
 [image]
Term
 This is a Nor Gate and is defined by the following[image] Is the nor gate associative
Definition
Term
 Consider three sets A, B, and C. The triple (A,B,C) is a function iff: ___[image]___ and for any u[image]____, if _____[image]____ and ______[image]_____ then v = w
Definition
 Consider three sets A, B, and C. The triple (A,B,C) is a function iff: C[image]AxB and for any u[image]A, if (u,v)[image]c and (u,W)[image]c then v = w
Term
 Consider The Function F, An element of the domain may have    No Image under F Exactly one image under F exactly two images under f
Definition
 It can only have    No Image under F Exactly one image under F
Term
 An Element of the codomain may have    No Image under F Exactly one image under F exactly two images under F
Definition
 It Can Have    No Image under F Exactly one image under F exactly two images under F
Term
 Consider the function f:[image] [image][image]                                 x [image]2x-3    0 has an image under f 1 has an image under f 2 has an image under f  0 has a preimage under f 1 has a preimage under f 2 has a preimage under f
Definition
 2 has an image under f  1 has a preimage under f
Term
 Consider a Function (A,B,C). The notation f(u) = v expresses the face that ____ [image] ___
Definition
 The notation f(u) = v expresses the face that (u,v) [image] C
Term
 Two functions (A,B,C) and (A',B',C') are equal iff A=A', B=B' and C = C' consider the function f: ℝ[image]ℝ                                                                                       x[image]1/x   g:ℝ[image]ℝ  y[image]1/y   g:ℝ*[image]ℝ  u[image]1/u   g:ℝ[image]ℝ  p[image]p/p2   g:ℝ[image]ℝ  z[image]z-1/z(z-1)
Definition
 g:ℝ[image]ℝ  p[image]p/p2   g:ℝ[image]ℝ  y[image]1/y
Term
 How many Functions from {0,1} to {0,1}
Definition
 There are 9
Term
 Consider natural numbers u,v,w,x,y such that y = ux2 + vx+w. if (uvw)x  is the base x expansion of y hen what is x greater then
Definition
 W x>0
Term
 (493)16 +(99)16 = (    )16
Definition
 (493)16 +(99)16 = (52C)16
Term
 What numbers are in the base 12
Definition
 0,1,2,3,4,5,6,7,8,9,A,B
Term
 what is (11001100)2 to the base 8
Definition
 (314)8
Term
 Convert (ABC)16 to the base 2 expansion
Definition
 (101010111100)2
Term
 If the rightmost digit in the base b expansion o f(2417)b X (37)b is 9 then b might be ?
Definition
 10 20 40
Term
 What is a Domain?
Definition
 A function is a relationship between two sets of numbers.   Notice that a function maps values to one and only onevalue. Two values in one set could map to one value, but one value must never map to two values: that would be a relation, not a function.
Term
 What is a Codomain?
Definition
 its basically the range.  In mathematics, the codomain or target set, of a function is the set Y into which all of the output of the function is constrained to fall. It is the set Y in the notation f: X→Y
Term
 A binary operation on a set S is?
Definition
 A Function from S2 to S such that every element of S2 has an image.
Term
 Let + be a binary operation on a set S and let e be an element of S. e is an absorbing element of + if?
Definition
 u+e=e+u  for any u in S
Term
 define distributive
Definition
 distributivity is a property of binary operations.  For example: 2 × (1 + 3) = (2 × 1) + (2 × 3)
Term
 Let + and X be two binary operations on a set S. + is a distributive over x if
Definition
 u+(uXw) = (u+v)X(u+w) and (vXw)+u = (v+u)X(w+u) for any u,v and w in S
Term
 Define the absorbing element?
Definition
 a special type of element of aset with respect to a binary operation on that set. The result of combining an absorbing element with any element of the set is the absorbing element itself.
Term
 What is the neutral element for addition
Definition
 0
Term
 what is the neutral element for multiplication?
Definition
 1
Term
 what is the absorbing element for addition?
Definition
 There is no absorbing element
Term
 what is the absorbing number for multiplication?
Definition
 0
Term
 What is the idempotent binary operation on the R
Definition
 Idempotent operations are operations that can be applied multiple times without changing the resul
Term
 Define Unary Operation
Definition
 a unary operation is an operation with only one operand, i.e. a single input. Specifically, it is a function [image]
Term
 What is De Morgan's Law
Definition
 the theorem of set theory that the complement of the intersection of two sets is equal to the union of the complements of the sets.   (x + y) = xy
Term
 state the Identity Law?
Definition
 the Identity law states that an object is the same as itself: A ≡ A. Any reflexive relation upholds the law of identity.?
Term
 State the commutative Law?
Definition
 commutativity is the property that changing the order of something does not change the end result. It is a fundamental prop   x+y =y+x x*y = y*x
Term
 State the associative law?
Definition
 It means that, within an expression containing two or more occurrences in a row of the same associative operator, the order in which the operations are performed does not matter as long as the sequence of the operands is not changed.   (x+y) +z = x+ (y +z) (x*y)*z = y*(x*z)
Term
 state the Distributive laws?
Definition
 we say that multiplication of real numbers distributes over addition of real numbers   x+y*z = x*(+4)(x+z) x*(y+z) = x*y+x*z
Term
 State the complement Law?
Definition
 set A refers to things not in (that is, things outside of), A. The relative complement of A with respect to a set B, is the set of elements in B but not in A.   x + [image] = 1 x*[image]=0
Term
 law of the double complement ?
Definition
 Acc  =  A
Term
 State of the domination laws?
Definition
 x+1 = 1 x*x=x
Term
 state the idempotent Law?
Definition
 Idempotent operations are operations that can be applied multiple times without changing the result.   x+x=x x*x=x
Term
 What is a Tautology?
Definition
 is a formula which is true in every possible interpretation
Term
 calculate the base 16 expansion of (1675)8  + (BF)16
Definition
 since (1)8=(001)2 and (6)8=(110)2 and (7)8 = (111)2 and (5)8 = (101)2 and added together you get (1675)8 =(001110111101)2 convert to 16 digest (3BD)16
Term
 In p[image]q, the proposition p is called the ____________ and the proposition q is called the ______________
Definition
 In p[image]q, the proposition p is called the hypothesis and the proposition q is called the conclusion
Term
 The converse of p[image]q is ______ and the contrapositive of p[image]q  is _____
Definition
 The converse of p[image]q is q[image]p and the contrapositive of p[image]q  is [image]p[image][image]q
Term
 |{}| =
Definition
 0
Term
 |{{},{}}| =
Definition
 1
Term
 2{}=
Definition
 {{}}
Term
 2{{}}=
Definition
 {{},{{}}}
Term
 Let S be a set if |s| is even then |s2| is even if |s2| is even then |s| is even if |s| is odd then |s2| is even if |s2| is even then |s| is odd
Definition
 the answer is if |s| is odd then |s2| is even
Term
 A Binary relation over two sets U and V is
Definition
 a triple (U,V,G) where G is the subset of UxV
Term
 A ternary relation over three sets U,V,and W is?
Definition
 A quadruple (U,V,W,G) where G is a subset of UxVxW
Term
 What is a subset?
Definition
 A is a subset of a set B if A is "contained" inside B. A and B may coincide.  [image]
Term
 If the graph f a binary relation R is {(1,a),(1,c),(3,b)(5,c)} then the graph of R-1 is
Definition
 {(a,1),(c,1),(1,c),(b,3)(c,5)}
Term
 We say R is Reflexive iff
Definition
 which every element is related to itself, i.e., a relation R on S where xRx holds true for every x in S   [image]
Term
 We say that R is symmetric iff
Definition
 [image] u [image]v (uRv [image] vRu)
Term
 We say that R is antisymmetric iff?
Definition
 [image] u [image]v (uRv [image] vRu) [image] u = v)
Term
 We say that R is transitive iff?
Definition
 [image] u [image]v [image]w (uRv [image] vRw) [image] uRw)
Term
 consider two binary relations R1 = (U,V,G1) and R2=(V,W,G2) The composite of R1 and R2 is R2[image]R1=(U,W,G) with G={(u,w) [image] UxW  | [image] ___________}
Definition
 R2[image]R1=(U,W,G) with G={(u,w) [image] UxW  | [image] v [image]  V,(uR1v [image]vR2W}
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