Truth Functional Logic — DU B.A. (Hons.) Philosophy Previous Year Question Papers

3. Q. (1) a. Determine the Validity/Invalidity of any two the following argument forms by Truth Table Method: 5x2=10 b. Determine the logical status of any one the following propositional forms: 5 Q. (2) a. Symbolize any four of the following: 8 i) Two triangles are formed if a square is divided diagonally. (T, i) Unless it rains in time, the harvest will not be good. (R, H) iii) Only if the rain stops will the match begin. (R, M) iv) She failed though she tried. (F, T) v) Either make haste and get ready soon or you will be late for college. (H, R, L) vi) It is not the case that neither the library nor the gym is open on Sunday. (L, G) vii) That you have a valid passport is a necessary condition for traveling abroad. (P,T) b. Prove the validity/invalidity of any two of the following by Reductio-ad-absurdum method: 5X2=10 0. 3) a. Rewrite the following into stroke function: 2.5 x2 = 5 b. Rewrite the following in terms of negation and dot (~, v): 2x2=4 Q.4) a. Construct a formal proof of validity for any one of the following by using suggested notation: 6 1) If we plant the trees now, we will benefit the future generations. We can devise methods by which the environment can be saved if we wish to benefit the future generations. Our devising methods by which the environment can be saved will cause the general well being of the people living in cities. Hence the general well being of people living in cities will follow from our planting the trees now. (P, B, D, C) ii) Napoleon is to be condemned if he usurped power that was not rightfully his own. Either Napoleon was a legitimate monarch or else he usurped power that was not rightfully his own. Napoleon was not a legitimate monarch. So Napoleon is to be condemned. (C, U, L) b. Construct a formal proof of validity for any one of the following: 6 Q.5) Using the strengthened rule of conditional proof, construct a proof of validity for any one of the following: Q.6) Construct an Indirect Proof of any one of the following: 6 Q.7) Translate any four of the following into the logical notation of propositional functions and quantifiers: i) Reporters are present. (Rx, Px) ii) Not any applicant was hired. (Ax, Hx) ili) Some foods are edible only if they are cooked.(Fx, Ex, Cx) iv) No car is safe unless it has good brakes. (Cx, Sx, Bx) v) The common cold is never fatal.(Cx, Ex) vi) Only Indian citizens can vote in Indian elections. (Cx, Ex) Q.8) Construct a Formal proof of validity for the following: 5+3=8 i) Only lawyers and politicians are members. Some members are not college graduates. Therefore, some lawyers are not college graduates. (Lx, Px, Mx, Cx) Only pacifists are Quakers. There are religious Quakers. Therefore, pacifists are sometimes religious. (Px, Qx, Rx) Q.9) Prove the invalidity of the following by constructing a model containing of two individuals. (Do any two (8marks)