Question: Let A = { 1, 2, 3, 4 } , and let R be the relation defined on A defined by R = {(1,1), (2,2), (3,3), (4,4), (1,2), (2,3), (3,4), (1,3), (2,4)}

(a) (5 points) Draw the digraph of this relation.

(b) (10 points) Which of the properties: reflexive, antisymmetric and transitive are true for the given relation? Begin your discussion by defining each term in general first and then show how the definition relates to this specific example.

(c) (5 points) Write the Boolean (yes/no) matrix of the relation, R, given above. g

(d) ( 5 points) Use the matrix of part (c) to determine the ordered pairs in the relation R².