Question

The relation "Is greater than" on the set {0, -1, 1} is an empty relation.

• A. True
• B. False

Answer 1

The correct option is B

False

We want to check if the relation “Is greater than” on the set {0,-1, 1} is an empty relation or if it has zero elements. We will first find the cartesian product and check if elements of any ordered pair is related through the relation “is greater than”. The cartesian product A $\times$ A is { (0,0), (0, -1), (0,1), (-1,0), (-1,-1), (-1,1), (1,0), (1,-1), (1,1)}. In this, elements like (0,-1) , where the first element is greater than the second, satisfies the relation “is greater than”. So we can say that it is not an empty relation.