2. Provide semi-formal Natural Deduction proofs of the following claims. You may only use the eight Natural Deduction inference rules. Remember that when writing semi-formal proofs for this class, you must follow the guidelines we discussed in the lectures. You can also find those guidelines in the lecture notes, so please use those as a reference. If your proofs do not follow those guidelines they will receive 0 points, and you will be asked to resubmit the assignment. (a) (PQ)R,PS,QR (b) (KL)N,KMNM (c) ABB(AC) (d) (AB)C,B,ADCD (e) (AB)C,B(AD)(CD) (f) P(QR)(PS)(RS) (g) X(X(ZY))XY (h) (X(X(ZY)))(XY) (i) PQ(PQ) (j) (WX)Y,X(WY)