Choose the correct statement about the empty relation on A={1,2,3}.
Answer and explanation
Correct answer: It is transitive
A relation is transitive if every occurrence of (a,b) and (b,c) implies (a,c). The empty relation contains no ordered pairs, so there is no pair of premises that can produce a counterexample. The implication is therefore true vacuously. This remains true even though A has three elements; the set need not be empty. Hence the empty relation is transitive, and option A is correct.
Frequently asked questions
What is the correct answer to this question?
It is transitive
Why is this the correct answer?
A relation is transitive if every occurrence of (a,b) and (b,c) implies (a,c). The empty relation contains no ordered pairs, so there is no pair of premises that can produce a counterexample. The implication is therefore true vacuously. This remains true even though A has three elements; the set need not be empty. Hence the empty relation is transitive, and option A is correct.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Transitive relation.
