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


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


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


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 R_{1}= ( U, V, G_{1}) and R_{2 }^{= (}V,W,G_{2})
What is the composite of R_{1 }and R_{2}? 

Definition
The Composite of R_{1} and R_{2} is R_{2 º }R_{1 }= (U,W,G) With G = {(u,w) [image] UxW [image]v [image]V,(uR_{1 }V vR_{2}w)} 


Term
Consider Two Binary relations R_{1}= ( U, V, G_{1}) and R_{2 }^{= (}V,W,G_{2})
What is R_{1 }[image] R_{2}? 

Definition
R_{1 }[image] R_{2 }= (U, V,G_{1 [image] G2)} 


Term
Let R be a binary relation on some set U
What is an example of Reflexove iff: 

Definition


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


Term
What type of gate is this
[image] 

Definition


Term
What type of gate is this
[image] 

Definition


Term
Solve this Circuit[image]


Definition


Term
This is a Nor Gate and is defined by the following[image]
Use Just Nor gate to form an [image]


Definition


Term
This is a Nor Gate and is defined by the following[image]
Use Just Nor gate to form an X+Y


Definition


Term
This is a Nor Gate and is defined by the following[image]
Use Just Nor gate to form an X[image]Y


Definition


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]2x3
 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/p^{2}
g:ℝ[image]ℝ
z[image]z1/z(z1)


Definition
g:ℝ[image]ℝ
p[image]p/p^{2}
g:ℝ[image]ℝ
y[image]1/y



Term
How many Functions from {0,1} to {0,1} 

Definition


Term
Consider natural numbers u,v,w,x,y such that y = ux^{2} + vx+w. if (uvw)_{x }is the base x expansion of y hen what is x greater then 

Definition


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


Term
Convert (ABC)_{16} to the base 2 expansion 

Definition


Term
If the rightmost digit in the base b expansion o f(2417)_{b }X (37)_{b} is 9 then b might be ? 

Definition


Term

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

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 S^{2} to S such that every element of S^{2} 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


Term

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


Term
what is the neutral element for multiplication? 

Definition


Term
what is the absorbing element for addition? 

Definition
There is no absorbing element 


Term
what is the absorbing number for multiplication? 

Definition


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

Definition
a unary operation is an operation with only one operand, i.e. a single input. Specifically, it is a function
 [image]



Term

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

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


Term
State of the domination laws? 

Definition


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

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


Term

Definition


Term

Definition


Term

Definition


Term
Let S be a set
 if s is even then s^{2} is even
 if s^{2} is even then s is even
 if s is odd then s^{2} is even
 if s^{2} is even then s is odd


Definition
the answer is if s is odd then s^{2} 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

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 R_{1} = (U,V,G_{1}) and R_{2}=(V,W,G_{2}) The composite of R_{1} and R_{2} is R_{2[image]R1=(U,W,G) with G={(u,w) [image] UxW  [image] ___________}}


Definition
R_{2[image]R1=(U,W,G) with G={(u,w) [image] UxW  [image] v [image] V,(uR1v [image]vR2W}} 

