i) Write the predicate formula for the definition of a relation on a set is transitive. Use predicate transitive(R;A) to denote relation R on set A is transitive and predicate member((x; y);R) to denote (x; y) 2 R.

ii) Apply the predicate formulas in i) to transitive( f(a; a); (b; b); (a; b); (b; a); (1; 1); (9; 9); (1; 9); (9; 1)g; fa; b; 1; 9g).

iii) How i) and ii) are related to the one-step backward for a primal concept we learned before?