1. Let M be the set {Neo, Morpheus, Trinity}. Give three dierent partitions of M

Question

1. Let M be the set {Neo, Morpheus, Trinity}. Give three dierent partitions of M.

2. Let C be the set { Gimli, Gandalf, Sauron, Saruman, Frodo }. Let T be an endorelation on the set C with the following elements: (Gimli, Gimli) (Gimli, Gandalf) (Gimli, Frodo) (Gandalf, Gandalf) (Gandalf, Gimli) (Gandalf, Saruman) (Saruman, Gandalf) (Gandalf, Frodo) (Frodo, Gimli) (Frodo, Gandalf) (Frodo, Frodo) (Sauron, Sauron)
a. Is T reexive? Why or why not?
b. Is T symmetric? Why or why not?
c. Is T antisymmetric? Why or why not?
d. Is T transitive? Why or why not?
5. Let U be the set of all UMW students. For each of the following relations (dened as a subset of U × U), specify whether (and why or why not) each of them is reexive, symmetric, antisymmetric, and/or transitive.
a. U isRoommateWith U • reexive?
• symmetric?
• antisymmetric?
• transitive?

5. Let U be the set of all UMW students. For each of the following relations (dened as a subset of U × U), specify whether (and why or why not) each of them is reexive, symmetric, antisymmetric, and/or transitive.
a. U isRoommateWith U • reexive?
• symmetric?
• antisymmetric?
• transitive?

c. U hasKissedOnTheLips U • reexive?
• symmetric?
• antisymmetric?
• transitive?

d. U hasReadMoreHarryPotterNovelsThan U • reexive?
• symmetric?
• antisymmetric?
• transitive?

e. U isSmarterThanInAtLeastOneAcademicSubject U • reexive?
• symmetric?
• antisymmetric?
• transitive?

Let R be the set of all recipes Betty likes, and I be the set of all ingredients at her grocery store. Further, let criticalIngredient be a relation between R and I with the following members: { (PeachCobbler, peaches), (ChickenKiev, breadCrumbs), (PeachCobbler, our), (Soue, eggYolks) }. Is criticalIngredient a function from R I? Why or why not?

Let P be the set of all UMW professors, and S the set of all UMW students. Further, dene a function faveUMWProfessor : S P. For example, faveUMWProfessor(RebeccaGraham) = DrFernsebner, and faveUMWProfessor(ElizabethRamsey) = DrMatzke. Is faveUMWProfessor injective? Surjective? Bijective? Explain.

Let A be the set of all airports in the world, and C the set of all three–letter airport codes. Further, dene a function codeOf : A C. For example, codeOf(ReaganNational) = DCA, and codeOf(TorontoPearsonInternational) = YYZ. Is codeOf injective? Surjective? Bijective? Explain.

Let N be the set of natural numbers, and R the set of real numbers. Further, let aSmidgenLessThan be a relation between R and N such that for every ordered pair p aSmidgenLessThan, the second element is the least natural number that is greater than or equal to the rst element. Is aSmidgenLessThan a function from RN? Why or why not?

Explanation / Answer

this question is too big and has lot of subparts. Can you please post 1 more questions.

1)

3 different partition can be done

{Neo, Morpheus}

{Neo, Trinity}

{Morpheus, Trinity}

2)

Yes it is reflexive as for all (a,b) present in this set (b,a) is also there.

example can be (Gandalf, Saruman) (Saruman, Gandalf)

T is not transitive

example one set is (Gimli, Gandalf) other set is (Gandalf, Saruman) so we should have set (Gimli, Saruman) which is not there.

It is not symmetric and anti-symmetric

as (saruamn,saruman) is not present.

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