TruthFunctional Logic — DU B.A. (Prog) Philosophy Previous Year Question Papers

1. Answer any three of the following: 6x3=18 (i) What is a proposition? Distinguish between a proposition and a sentence with examples. (ii) Briefly distinguish between a statement form and an argument form. (iii) What is the use of 'either - or' (Disjunction) and "if-then' (Material Implication) in symbolic logic? Explain. (iv) Write a brief note on Relevance of Symbolic Logic. 2. (a) Answer any Two of the following: 3x2=6 (i) Define P=Q into "'and " (ii) Define (p > 9) V~r into '~' and "' (iii) Define ~ (p > q) > r into '"' and 'V' (b) If A, B and C are true statements and X, Y and Z are false statements, determine which of the following are true statements, Answer any three. 2x3=6 (c) Symbolize any three of the following : 2x3=6 If he is a good doctor, then he will definitely treat the patient. (G,P) ii. Neither Vikram nor Manoj are good dancers. (V, M) ili. Both tea and coffee are popular beverages. (T,C) iv. Soldiers are the backbone of the country, yet most deprived ones in comparison to others. V. You will get selected if and only if you work hard. (S, W) 3. (a) Use truth table method to test the validity/ invalidity of any ONE of the following arguments : (6) (b) Use truth table method to determine whether the following are tautologous, self-contradictory or contingent (any one) (6) (c) Prove the validity/invalidity of any two of the following by Shorter Truth Table 4. Using only the rules of inference and replacement, construct a formal proof of validity of the following. (any three) 6x3=18 5. (a) Symbolize the following sentences by using suggested notations of propositional functions and quantifiers. (any Three) i. Nurses are always considerate. (Nx, Cx) Reporters are present. (Rx, Px) iii. None but the brave deserves the fair. (Bx, Dx) iv. No boy scout ever cheats. (Bx, (x) V. Snake bites are sometimes fatal. ( Sx, Fx) vi. Indians are rarely punctual. (Ix, Px) (b) Answer the following questions: 6+6=12 Discuss the additional rules of Inference in Quantification Theory. (ii) Illustrate the free and bound variable along with individual constants with reference to theory of Quantification. Construct a Formal Proof of validity of the following.