Ex . 4. Prove that the following arguments are valid by constructing a deduction using the rules MP, MT, DN, Conj, Simp, CS, Disj, DS, DM, CP, and HS: (a) (A VB ) - C .. A - C (b) A - B, C - -B . A - -C (c) (A & B) - (F & G) .. -(F & G) - (-A V -B) (d) A - (B - C) . B - (A - C) (e) (A & B) - C . A - (B -C) (f) (( A VC) VD) - (C VE) .. A - (CVE) (g) A - (B & F ) , - F V ( B - G) .. A - G (h) B - (C & D) .. (B - C) & (B - D) (i) - (M V - S) , S - (R - M ) . A - (-RVT) (j) F - (A V B), - A & ((C V D ) - F) .. - B - -C (k) A - B . (C - A) - (C - B) (1 ) A - F, G & -A .. -(F & G) - -A (m ) (B & C) - -A, A - C . A - -B ( n ) T - - B, T - - D .T - -(B VD) (0 ) F - (G & H ) .. F - (GVI)