Binary relations

1. Write out sets of ordered pairs which constitute relations with the following properties and find predicates which express these relations:
   1. reflexive, transitive, not symmetric;
   2. symmetric, transitive, not reflexive;
   3. asymmetric, non-transitive.
2. Indicate the properties of the following relations:
   1. `x is a brother of y' in the domain of living people;
   2. `x semantically entails y' in the domain of the formulae of the language of propositional logic L₁;
   3. `x is capable of capturing y' in the domain of chess pieces in all possible chess positions.