A logic circuit realizing the function f has four inputs a, b, c, d. The three inputs a, b, and c are the binary representation of the digits 0 through 7 with a being the most significant bit. The input d is an odd-parity bit; that is, the value of d is such that a, b, c, and d always contains an odd number of 1's. (For example, the digit 1 is represented by abc = 001 and d = 0, and the digit 3 is represented by abcd = 0111.) The function f(a,b,c,d) has value 1 if the input digit is a prime number. (A number is prime if it is divisible only by itself and 1; 1 is considered to be prime, and 0 is not.)

Which of the following is true for f ?

(A). F has 5 prime implicants and 5 essential prime implicants.

(B). F has 2 prime implicants and 2 essential prime implicants.

(C). F has 3 prime implicants and 2 essential prime implicants.

(D). F has 5 prime implicants and 0 essential prime implicants.