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