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:

There are 5 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

8th Question is not from this topic

in this page question number 8 is question of DBMS subject of topic Joins.

Question Shifted to DBMS