# Relation

 Question 1
A relation $R$ is said to be circular if $aRb$ and $bRc$ together imply $cRa$.
Which of the following options is/are correct?
 A If a relation S is reflexive and symmetric, then S is an equivalence relation. B If a relation S is circular and symmetric, then S is an equivalence relation. C If a relation S is reflexive and circular, then S is an equivalence relation. D If a relation S is transitive and circular, then S is an equivalence relation.
GATE CSE 2021 SET-1   Discrete Mathematics
Question 1 Explanation:
 Question 2
Let $R$ be the set of all binary relations on the set {1,2,3}. Suppose a relation is chosen from $R$ at random. The probability that the chosen relation is reflexive (round off to 3 decimal places) is ______.
 A 0.25 B 0.125 C 0.465 D 0.565
GATE CSE 2020   Discrete Mathematics
Question 2 Explanation:

 Question 3
Let G be an arbitrary group. Consider the following relations on G:

R1: $\forall a,b \in G, aR_1b$ if and only if $\exists g \in G$ such that $a=g^{-1}bg$
R2: $\forall a,b \in G, aR_2b$ if and only if $a=b^{-1}$

Which of the above is/are equivalence relation/relations?
 A R1 and R2 B R1 only C R2 only D Neither R1 nor R2
GATE CSE 2019   Discrete Mathematics
Question 3 Explanation:
 Question 4
The time complexity of computing the transitive closure of binary relation on a set of n elements is known to be
 A O(n) B $O(n * \log (n))$ C $O\left(n^{\frac{3}{2}}\right)$ D $O\left(n^{3}\right)$
ISRO CSE 2018   Discrete Mathematics
Question 4 Explanation:
 Question 5
The time complexity of computing the transitive closure of a binary relation on a set of $n$ elements is known to be
 A $O(n \log n)$ B $O\left(n^{3 / 2}\right)$ C $O\left(n^{3}\right)$ D $O(n)$
ISRO CSE 2017   Discrete Mathematics
Question 5 Explanation:

There are 5 questions to complete.

### 6 thoughts on “Relation”

1. In the question 23, please update the correct option to B

• Thank You MOUNIKA DASA,