I. Let each of R, S, and T be binary relations on N2 as defined here: R-[<m, n EN nis the smallest prime number greater than or equal to m] S -[< m, n> EN* nis the greatest prime number less than or equal to m] (a) Which (if any) of these binary relations is a (unary) function? (b) Which (if any) of these binary relations is an injection? (c) Which (if any) of these binary relations is a surjection? (d) For each of these relations, specify which (if any) of the following properties it satisfies reflexivity, irreflexivity, symmetry, asymmetry, anti-symmetry, transitivity (e) For each of these relations, specify each of the following (i) the inverse relation, (ii) the reflexive closure, (iii) the symmetric closure, and (iv) the transitive closurc. (!) Lt A { < 1, 2 , < 1, 3 ), < 2, 3 , . 3, 7 ) }. Specify (i) the transitive closure of the symmetric closure of the relation A, and (ii) the symmetric closure of the transitive c 1 osure. Every equivalence relation induces a unique partition of the domain of the relation. Consider the following partition of the set B-[ 0, 1, 2, 3, 4 Give an explicit specification of the equivalence relation associated with this partition of B.