answer and explain this problem

Consider a cryptosystem with P={a,b,c},K={K1,K2,K3}, and C={1,2,3,4}. Suppose the encryption function is as follows: Given that the keys are chosen equally likely, and the plaintext probability distribution is Pr[a]=1/2, Pr[b]=1/3, and Pr[c]=1/6,(i) either prove or disprove that the cryptosystem is perfectly secret, and (ii) compute H(P),H(K), and H(C). For (i), Show everything you have computed until a conclusion can be made. For (ii), around to 3 digits after the decimal points