Question

Let F be the relation on the set of commercial airports defined by:

If x and y are two such airports, xRy if there is a commercial flight that flies from A directly to B (non-stop).

Check all properties that the relation has and use common sense.

Anti-symmetric

Transitive

Reflexive

Symmetric

Answer 1

The relationship is not antisymmetric

The relationship is transitive

The relationship is not reflective

The relationship is symmetric

Explanation:

Anti-symmetric:

The antisymmetric property means that if A and B are two different airports, then there are no commercial flights from A to B or there are no commercial flights from B to A. There is no reason to think that this is true. Therefore, the antisymmetric property is fulfilled by the relationship.

Transitive:

Transitive ownership means that if A, B and C are three different airports, then if there are commercial flights from A to B and also from B to C, it implies that there must be commercial flights from A to C. There is no reason to think that this It can't be true. Therefore, the transitive property is fulfilled by the relationship.

Reflexive:

Reflective ownership means that if A is an airport, then there are commercial flights from A to A. There is no way this is true. Therefore, the reflexive property is not fulfilled by the relationship.

Symmetric:

Symmetric ownership means that if A and B are two different airports, then there are commercial flights from A to B implies that there are also commercial flights from B to A. There is no reason to think that this is not true. Therefore, the symetric property is fulfilled by the relationship.