Question

Let X,Y be discrete random variables related as Y=g(X), where g is a deterministic function. The ordering of their entropies satisfies

H(X)≤H(Y), equality holds if g is a one to one mapping

H(X)≥H(Y), equality holds if g is a one to one mapping

H(X)≤H(Y), equality holds when H(X|g(X))=0

H(X)≥H(Y), equality holds when H(X|g(X))=0