Binary Relations : Reflexive and Transitive, but not Antisymmetric

Give an example of or else prove that there are no relations on {a,b,c} that is reflexive and transitive, but not antisymmetric.

Binary Relations : Symmetric and Transitive, but not Reflexive

Give an example of or else prove that there are no relations on {1,2} that is symmetric and transitive, but not reflexive.

Hasse Diagram : Ordered Pairs and Boolean Matrix

Consider the following Hasse diagram of a partial ordering relation R on a set A: (see attached for image) (a) List the ordered pairs that belong to the relation. (b) Find the (boolean) matrix of the relation.

Reflexive, Antisymmetric and Transitive Properties : Hasse Diagram and Boolean Matrix

Please see the attached file for the fully formatted problems. Let A = {1, 2, 3, 4, 5, 6,12} and define the relation R on A by m R n iff m|n. Write the definitions of the properties, reflexive, antisymmetric and transitive and the use the definitions to determine whether each property holds for this relation. (a) Is this relation a partial ordering relation? Why? If so, draw its Hasse diagram. (b)Write the (boolean, that is the yes/no) matrix of this relation.

Hasse Diagram : Ordered Pairs and Boolean Matrix

Please see the attached file for the fully formatted problems. Consider the following Hasse Diagram of a partial ordering relation R on a set A. 5 / 3 / 4 | | 1| |2 a) List the ordered pairs belonging to the relation. b) Find the Boolean matrix of the relation.