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?

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?

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?

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")

(u,v)   G

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?

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?

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?

Consider Two Binary relations R₁= ( U, V, G₁) and R₂ ^{= (}V,W,G₂)

What is the composite of R₁ and R₂?

Consider Two Binary relations R₁= ( U, V, G₁) and R₂ ^{= (}V,W,G₂)

What is R₁   R₂?

Let R be a binary relation on some set U

What is an example of Reflexove iff: 

Using the following graph adjustx to show reflexive closure?

Using the following graph adjusts to show transitive closure?

What type of gate is this

What type of gate is this

What type of gate is this

Solve this Circuit 

This is a Nor Gate and is defined by the following

Use Just Nor gate to form an 

This is a Nor Gate and is defined by the following

Use Just Nor gate to form an X+Y

This is a Nor Gate and is defined by the following

Use Just Nor gate to form an XY

Consider The Function F, An element of the domain may have 

1. No Image under F
2. Exactly one image under F
3. exactly two images under f

It can only have 

• No Image under F
• Exactly one image under F

An Element of the codomain may have 

1. No Image under F
2. Exactly one image under F
3. exactly two images under F

It Can Have 

• No Image under F
• Exactly one image under F
• exactly two images under F

Consider the function f: 

                                x 2x-3 

1. 0 has an image under f
2. 1 has an image under f
3. 2 has an image under f 
4. 0 has a preimage under f
5. 1 has a preimage under f
6. 2 has a preimage under f

2 has an image under f 

1 has a preimage under f

Consider a Function (A,B,C).

The notation f(u) = v expresses the face that ____  ___

Two functions (A,B,C) and (A',B',C') are equal iff A=A', B=B' and C = C' consider the function f: ℝℝ

                                                                                      x1/x

g:ℝℝ

 y1/y

g:ℝ*ℝ

 u1/u

g:ℝℝ

 pp/p²

g:ℝℝ

 zz-1/z(z-1)

g:ℝℝ

 pp/p²

g:ℝℝ

 y1/y

W

x>0

• 10
• 20
• 40

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.

What is a Codomain?

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

distributivity is a property of binary operations.

 For example:

2 × (1 + 3) = (2 × 1) + (2 × 3)

Let + and X be two binary operations on a set S.

+ is a distributive over x if 

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

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

State the commutative Law?

 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

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)

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

 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 +  = 1

x*=0

x+1 = 1

x*x=x

 Idempotent operations are operations that can be applied multiple times without changing the result.

x+x=x

x*x=x

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

The converse of pq is ______

and the contrapositive of pq  is _____

Let S be a set

1. if |s| is even then |s²| is even
2. if |s²| is even then |s| is even
3. if |s| is odd then |s²| is even
4. if |s²| is even then |s| is odd

 A is a subset of a set B if A is "contained" inside B. A and B may coincide.

which every element is related to itself, i.e., a relation R on S where xRx holds true for every x in S

 u v (uRv  vRu)  u = v)

consider two binary relations R₁ = (U,V,G₁) and R₂=(V,W,G₂) The composite of R₁ and R₂ is R_{2R1=(U,W,G) with G={(u,w)  UxW  |  ___________}}