Please answer each question in its entireity Select ALL THAT

Please answer each question in its entireity. 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

Question 2

Solution

Question 2.

It is not reflexive as a,a and b,b are not in the relation

It is symmetric as for each x,y there is y,x in the relation

It is not transitive as a,b and b,a are there but a,a is not there

It is symmetric and hence not antisymmetric

Question 3

It is not reflexive as a,a is not present

It is transitive

It is not symmetric

It is antisymmetric as for no x,y is y,x present

Question 4

It is not reflexive

It is not transitive

It is not symmetric

It is antisymmetric

Question 5

It is not reflexive

It is not transitive as b,c and c,d are there but not b,d

It is not symmetric

It is not antisymmetric

Question 6

A sorted program runs faster

Queries run faster

There is less chance of losing data

A report is easier to read when printing out