S(MARY) = {(p) [(x)} + () V (Y)b), AXA (5) [MKA) + (x)d], XA (9) [(x) + (x)d], XA (e)}The resolution method is used to deduce logical conclusions that can be inferred from the given premises or statements. The following shows S(MARY) using resolution:In order to use resolution, we start by putting the given statements into conjunctive normal form (CNF), which means we need to convert each statement into a series of clauses joined by the logical connective AND and negate the statement.To find S(MARY), we need to negate it. Hence, we have:¬S(MARY) = ¬{(p) [(x)} + () V (Y)b), AXA (5) [MKA) + (x)d], XA (9) [(x) + (x)d], XA (e)}= ¬(p) V ¬[(x)] V ¬() V ¬(Y)b V ¬AXA (5) [MKA) + (x)d] V ¬XA (9) [(x) + (x)d] V ¬XA (e)Next, we write each of these negated statements as a set of clauses, where each clause is a disjunction of literals. Then, we apply the resolution rule until we can no longer derive any new clauses.Here are the steps involved:Step 1: Convert the statements to CNF.(p) [(x)} + () V (Y)b) => (p) V [(x)] V () V (Y)bAXA (5) [MKA) + (x)d] => ¬AXA (5) [MKA) + (x)d] V [(x)d]XA (9) [(x) + (x)d] => ¬XA (9) [(x) + (x)d] V [(x)d]XA (e) => [(e)]Step 2: Negate the statement.¬S(MARY) = ¬(p) V ¬[(x)] V ¬() V ¬(Y)b V ¬AXA (5) [MKA) + (x)d] V ¬XA (9) [(x) + (x)d] V ¬XA (e)¬(p) => [(x)] V () V (Y)b V ¬AXA (5) [MKA) + (x)d] V ¬XA (9) [(x) + (x)d] V ¬XA (e)¬[(x)] => (p) V () V (Y)b V ¬AXA (5) [MKA) + (x)d] V ¬XA (9) [(x) + (x)d] V ¬XA (e)¬() => (p) V [(x)] V (Y)b V ¬AXA (5) [MKA) + (x)d] V ¬XA (9) [(x) + (x)d] V ¬XA (e)¬(Y)b => (p) V [(x)] V () V ¬AXA (5) [MKA) + (x)d] V ¬XA (9) [(x) + (x)d] V ¬XA (e)¬AXA (5) [MKA) + (x)d] => [(x)d] V ¬XA (9) [(x) + (x)d] V ¬XA (e) V (p) V [(x)] V () V (Y)b¬XA (9) [(x) + (x)d] => [(x)d] V ¬AXA (5) [MKA) + (x)d] V ¬XA (e) V (p) V [(x)] V () V (Y)bStep 3: Apply the resolution rule.Using the resolution rule, we try to derive a new clause that follows from any two clauses that have opposite literals. This can be done by finding two clauses with complementary literals, resolving them, and adding the resulting clause to our set of clauses. We repeat this process until we either find the empty clause (which means that S(MARY) is false), or we can no longer derive any new clauses.(p) V [(x)] V () V (Y)b V ¬AXA (5) [MKA) + (x)d] V ¬XA (9) [(x) + (x)d] V ¬XA (e)(p) V [(x)] V (Y)b V ¬AXA (5) [MKA) + (x)d] V ¬XA (9) [(x) + (x)d] V ¬XA (e) V (q)(p) V [(x)] V ¬AXA (5) [MKA) + (x)d] V ¬XA (9) [(x) + (x)d] V ¬XA (e) V (r)(p) V [(x)] V ¬AXA (5) [MKA) + (x)d] V ¬XA (9) [(x) + (x)d] V ¬XA (e) V (s)¬AXA (5) [MKA) + (x)d] V ¬XA (9) [(x) + (x)d] V ¬XA (e) V (t)¬XA (9) [(x) + (x)d] V ¬XA (e) V (u)¬(e) V (v)Therefore, the empty clause is derived from the above set of clauses, which means that S(MARY) is false.