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) [image]  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  [image] 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?

[image]

Using the following graph adjusts to show transitive closure?

[image]

What type of gate is this

[image]

What type of gate is this

[image]

What type of gate is this

[image]

Solve this Circuit[image] 

This is a Nor Gate and is defined by the following[image]

Use Just Nor gate to form an [image]

This is a Nor Gate and is defined by the following[image]

Use Just Nor gate to form an X+Y

This is a Nor Gate and is defined by the following[image]

Use Just Nor gate to form an X[image]Y

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:[image] [image][image]

                                x [image]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 ____ [image] ___

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)

g:ℝ[image]ℝ

 p[image]p/p²

g:ℝ[image]ℝ

 y[image]1/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

[image]

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 + [image] = 1

x*[image]=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 p[image]q is ______

and the contrapositive of p[image]q  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.

 [image]

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

[image]

[image] u [image]v (uRv [image] vRu) [image] u = v)

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