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 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
0.250
B
0.125
C
0.465
D
0.565
GATE CSE 2020   Discrete Mathematics


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 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 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


There are 5 questions to complete.

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