CISC 1400 Discrete Structures Fall, 2020
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CISC 1400 Discrete Structures Fall, 2020
CISC 1400 — Discrete Structures Fall, 2020
Homework Assignment #4 (Relation)
1 Consider the following rules on the set of natural numbers, N, 1) write down 5 ordered pairs of natural numbers that are related under the relation, and 2) decide for the properties of reflexiveness (and irreflexiveness), symmetry (and antisymmetry) and transitivity. Note: please specify explicitly whether the relation has each of the five properties or not, and explain your answer.
(a) “is less than or equal to”
(b) “is a factor of”
(c) “is 3 less than”
2 Consider the following rules on the set of all Fordham students and examine the resulting relation for the properties of reflexiveness (and irreflexiveness), symmetry(and anti-symmetry) and transitivity.
(a) “went to the same high school as” (assuming everyone went to high schools, and some might have gone to multiple high schools).
(b) “share a same facebook friend with” (assuming every Fordham student is a Facebook user).
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CISC 1400 Discrete Structures Fall, 2020
3 Examine each of the following relations, and decide whether they are reflexive, irreflexive, symmetric, anti-symmetric, and transitive.
(a) R1 = {(x,y) ∈N ×N : (x − y) is odd}
(b) R2={(x,y)∈N×N:2x≤y}
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(c) R3 = {(a,b) ∈N×N : a and b are coprime with each other (i.e., the greatest common divisor of a and b is 1}.
4 Pickanonlineservicethatprovidescertainkindsofsocialnetworkingservice(suchasFacebook,twitter, LinkIn, ancestry, …) as your case studies, and perform some background research to find out the following:
(a) For the underlying relation(s) that the social networking service keeps track, how large is the user base (i.e., how many users does the service has)? (Please cite your source).
- (b) Whatkindofdiscoveryservicesdoesthesiteprovideforitsusers?(e.g.,Facebooksuggestspossible friends to its users). Make a guess at how it works.
- (c) Could you suggest new services for the site? Or do you have any hypothesis about the network that is formed using the service (e.g., six-degree of separation)?
CISC 1400 Discrete Structures Fall, 2020
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