###### Question 2603 – KVS 30-12-2018 Part-A

May 10, 2024###### Question 10814 – APPSC-2016-DL-CS

May 10, 2024# Question 10812 – APPSC-2016-DL-CS

Which of the following options is TRUE with regard to a relation R defined on ordered pairs of integers as given below: (x,y) R (low,up) if x>low and y<up?

Correct Answer: D

Question 10 Explanation:

If a relation is equivalence then it must be

i) Symmetric

ii) Reflexive

iii) Transitive

If a relation is a partial order relation then it must be

i) Reflexive

ii) Anti-symmetric

iii) Transitive

If a relation is total order relation then it must be

i) Reflexive

ii) Symmetric

iii) Transitive

iv) Comparability

Given ordered pairs are (x,y)R(low,up) if (x,up).

Here < , > are using while using these symbols between (x,y) and (y,up) then they are not satisfy the reflexive relation. If they use (x< =low) and (y >=low) then reflexive relation can satisfies.

So, given relation cannot be an Equivalence. Total order relation or partial order relation.

i) Symmetric

ii) Reflexive

iii) Transitive

If a relation is a partial order relation then it must be

i) Reflexive

ii) Anti-symmetric

iii) Transitive

If a relation is total order relation then it must be

i) Reflexive

ii) Symmetric

iii) Transitive

iv) Comparability

Given ordered pairs are (x,y)R(low,up) if (x,up).

Here < , > are using while using these symbols between (x,y) and (y,up) then they are not satisfy the reflexive relation. If they use (x< =low) and (y >=low) then reflexive relation can satisfies.

So, given relation cannot be an Equivalence. Total order relation or partial order relation.

R is totally ordered

R is partially ordered but not totally ordered

R is an equivalence relation

R is neither partially ordered nor an equivalence relation

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