See Question.pdf
Subject
Computer Science Discrete Math
Question
Solution Preview
This material may consist of step-by-step explanations on how to solve a problem or examples of proper writing, including the use of citations, references, bibliographies, and formatting. This material is made available for the sole purpose of studying and learning - misuse is strictly forbidden.
9)
We need to prove the relation is reflexive, symmetric and transitive.
For reflexivity, this means (a,b) R (a,b) This is true since a*b=b*a => R is reflexive.
For symmetry, this means if (a,b) R (c,d), then ad=bc.
On the other hand, cb=da (we reverted the order)=> (c,d) R (a,b)=> R is a symmetric relation.
For transitivity, we assume that (a,b) R (c,d) and also (c,d) R (e,f).
In this case it means that ad=bc and also cf=de
We multiply the two equalities side by side => adcf=bcde => adcf-bcde=0=> (af-be)cd=0...
We need to prove the relation is reflexive, symmetric and transitive.
For reflexivity, this means (a,b) R (a,b) This is true since a*b=b*a => R is reflexive.
For symmetry, this means if (a,b) R (c,d), then ad=bc.
On the other hand, cb=da (we reverted the order)=> (c,d) R (a,b)=> R is a symmetric relation.
For transitivity, we assume that (a,b) R (c,d) and also (c,d) R (e,f).
In this case it means that ad=bc and also cf=de
We multiply the two equalities side by side => adcf=bcde => adcf-bcde=0=> (af-be)cd=0...
Related Homework Solutions
Discrete Mathematics Problem
$10.00
Discrete Mathematics
Division Algorithm
Computer Science
Primes
Proof
Integers
Discrete Math Exercises with Functions
$10.00
Function
Domain
Range
Solution
One-to-one
Onto
Set
Target
Equation
Codomain
Computer Science
Discrete Math
Questions Involving Functions: One-to-one, Onto, Inverse, Composition, Examples
$30.00
Question
Function
One-to-one
Onto
Map
Inverse
Compose
Identity
Rule
Counterexample
Real
Projection
Coordinate
Set
Diagram
Question
Function
One-to-one
Onto
Map
Inverse
Compose
Identity
Rule
Counterexample
Real
Projection
Coordinate
Set
Diagram
Discrete Math Questions
$10.00
Recurrence
Array
Arithmetic
Sequence
Progression
Polynomial
Relation
Generating
Function
Prime Numbers, Numeration Bases & Euclidean Algorithm
$18.00
GCD
Euclidean Algorithm
Prime
Base
Division
Binary
Octal
Hexadecimal
Computer Science
Discrete Math
Discrete Math Problems and Solutions
Return to homework library