2. (a) State all the natural deduction rules for implication and conjunction. [10 marks] (b) Use the natural deduction rules to derive the following judgements: i. (P and Q) implies (Q and P) ii. FP implies (P implies Q) implies Q) [15 marks] (c) For each of the algorithms below, calculate how many times the code A is executed, and how many times the code B is executed. for i=1 to n do for j1 to n do if i=j then A else B for i + 1 to n do for j ti to n do if i