Question: Let A = {x, a, b, c, d}. (a) How many closed binary operations f on A satisfy f(a, b) = c? (b) How many

Let A = {x, a, b, c, d}.
(a) How many closed binary operations f on A satisfy f(a, b) = c?
(b) How many of the functions f in part (a) have x as an identity?
(c) How many of the functions f in part (a) have an identity?
(d) How many of the functions f in part (c) are commutative?

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