Let S = {0, 1, 2, 3, 4}. Let R be the binary relation on S such that aRb if and only if a + b = 3 and a ≤ b.

(a) Write this relation down as a subset of the Cartesian product S x S.

I believe this is R = {(0, 3), (1, 2)}.

(b) What is the adjacency matrix of this relation?

Adjacency matrix should be full of zeroes... aside from row = 0, column = 3 (entry of 1) and row = 1, column = 2 (entry of 1). The rest are just zeroes.

(c) What is the arrow diagram of this relation?

Not sure about this.

(d) What is the digraph of this relation?

Not sure about this.

Cheers for assistance.