Please answer each question in its entirity Select ALL THAT

Please answer each question in its entirity. Select ALL THAT APPLY FOR EACH QUESTION.

What are the proporties of the following relation

{ <a,b>, <b,a>, <c,c>}

CHECK ALL THAT APPLY

Reflexive

Transitive

Symmetric

Antisymmetric

None of the above.

What are the proporties of the following relation

{ <a,b>, <b,b>, <a,c>, <c,b>}

CHECK ALL THAT APPLY

Reflexive

Transitive

Symmetric

Antisymmetric

None of the above.

What are the proporties of the following relation

{ <a,b>, <b,c>, <c,d>, <d,e>}

CHECK ALL THAT APPLY

Reflexive

Transitive

Symmetric

Antisymmetric

None of the above

What are the proporties of the following relation

{ <a,b>, <b,c>, <c,d>, <a,c>, <a,a>,<b,b> }

Check all that apply.

Reflexive

Transitive

Symmetric

Antisymmetric

None of the above

In the sub-module on relations, we discussed total orders. Total orders allow you to sort the elements in a list. Why is sorting such an important operation in computing?

CHOOSE ALL THAT APPLY

A sorted program runs faster

Queries run faster

There is less chance of losing data

A report is easier to read when printing out

Solution

a. { <a,b>, <b,a>, <c,c>}

it is symmetric since all the components of type (x1,x2) and (x2,x1) are present throughout the set.

b. { <a,b>, <b,b>, <a,c>, <c,b>}

it is antisymmetric since if (x1,x2) is present then

(x2,x1) is definitely not present throughout the set.

c.{ <a,b>, <b,c>, <c,d>, <d,e>}

it is antisymmetric since if (x1,x2) is present then

(x2,x1) is definitely not present throughout the set.

d.{ <a,b>, <b,c>, <c,d>, <a,c>, <a,a>,<b,b> }

here none of the above reasons clearly qualifies hence none of the above is suited here.