Which of the following relations are equivalent?
Which of the following relations are equivalent?
The correct option is A Let two people be related if and only if they are friends
If A and B are friends and B and C are also friends, can we say that A and C would also be friends? Not always, right? So the first relation is not transitive.
The case of half siblings is also similar to the case of friends. It won't be transitive.
We saw that empty relation is not reflexive because there won't be element in empty relation and no element will be connected any element.
Universal relation defined on any set A is an equivalence relation. This is because, it will have all the possible elements or all the elements in the cartesian product, making it reflexive, symmetric and transitive at the same time. So there is only one relation which is equivalence out of the four relations given to u
Let two people be related if and only if they are friends
If A and B are friends and B and C are also friends, can we say that A and C would also be friends? Not always, right? So the first relation is not transitive.
The case of half siblings is also similar to the case of friends. It won't be transitive.
We saw that empty relation is not reflexive because there won't be element in empty relation and no element will be connected any element.
Universal relation defined on any set A is an equivalence relation. This is because, it will have all the possible elements or all the elements in the cartesian product, making it reflexive, symmetric and transitive at the same time. So there is only one relation which is equivalence out of the four relations given to u
