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?
Which of the following options is/are correct?
If a relation S is reflexive and symmetric, then S is an equivalence relation. | |
If a relation S is circular and symmetric, then S is an equivalence relation. | |
If a relation S is reflexive and circular, then S is an equivalence relation. | |
If a relation S is transitive and circular, then S is an equivalence relation. |
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 ______.
0.250 | |
0.125 | |
0.465 | |
0.565 |
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?
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?
R1 and R2 | |
R1 only | |
R2 only | |
Neither R1 nor R2 |
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
O(n) | |
O(n * \log (n)) | |
O\left(n^{\frac{3}{2}}\right) | |
O\left(n^{3}\right) |
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
O(n \log n) | |
O\left(n^{3 / 2}\right) | |
O\left(n^{3}\right) | |
O(n) |
Question 5 Explanation:
Question 6 |
A binary relation R on \mathbb{N}\times \mathbb{N} is defined as follows: (a,b)R(c,d) if a \leq c
or b \leq d. Consider the following propositions:
P: R is reflexive
Q: R is transitive
Which one of the following statements is TRUE?
P: R is reflexive
Q: R is transitive
Which one of the following statements is TRUE?
Both P and Q are true | |
P is true and Q is false. | |
P is false and Q is true | |
Both P and Q are false |
Question 6 Explanation:
Question 7 |
Let R be a relation on the set of ordered pairs of positive integers such that ((p,q),(r,s)) \in R if and only if p-s=q-r. Which one of the following is true about R?
Both reflexive and symmetric | |
Reflexive but not symmetric | |
Not reflexive but symmetric | |
Neither reflexive nor symmetric |
Question 7 Explanation:
Question 8 |
Consider two relations R1(A,B) with the tuples (1,5), (3,7) and R2(A,C) = (1,7), (4,9). Assume that R(A,B,C) is the full natural outer join of R1 and R2. Consider the following tuples of the form (A,B,C): a = (1,5,null), b = (1,null,7), c = (3, null, 9), d = (4,7,null), e = (1,5,7), f = (3,7,null), g = (4,null,9). Which one of the following statements is correct?
R contains a, b, e, f, g but not c, d. | |
R contains all of a, b, c, d, e, f, g. | |
R contains e, f, g but not a, b. | |
R contains e but not f, g. |
Question 8 Explanation:
Question 9 |
Let R be the relation on the set of positive integers such that aRb if and only if a and b are distinct and have a common divisor other than 1. Which one of the following statements about R is true?
R is symmetric and reflexive but not transitive | |
R is reflexive but not symmetric and not transitive | |
R is transitive but not reflexive and not symmetric | |
R is symmetric but not reflexive and not transitive |
Question 9 Explanation:
Question 10 |
Consider the binary relation R = {(x,y), (x,z), (z,x), (z,y)} on the set {x,y,z}.
Which one of the following is TRUE?
R is symmetric but NOT antisymmetric | |
R is NOT symmetric but antisymmetric | |
R is both symmetric and antisymmetric | |
R is neither symmetric nor antisymmetric |
Question 10 Explanation:
There are 10 questions to complete.
In the question 23, please update the correct option to B
Thank You MOUNIKA DASA,
We have updated the answer.
8th q not from Set theory