TW-TST 1994 Problem 5

Given $X=\{0,a,b,c\}$ , let $M(X)=\{f|f: X\to X\}$ denote the set of all functions from $X$ into itself. An addition table on $X$ is given us follows: $+$ $0$ $a$ $b$ $c$ $0$ $0$ $a$ $b$ $c$ $a$ $a$ $0$ $c$ $b$ $b$ $b$ $c$ $0$ $a$ $c$ $c$ $b$ $a$ $0$ a)If $S=\{f\in M(X)|f(x+y+x)=f(x)+f(y)+f(x)\forall x,y\in X\}$ , find $|S|$ . b)If $I=\{f\in M(X)|f(x+x)=f(x)+f(x)\forall x\in X\}$ , find $|I|$ .