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

1. Explain the following with examples: (Any Three) (6x3=18) (a) Uses of symbols (b) Two senses of 'either...or (c) Material Implication (d) Truth and Validity 2 (a) Using the truth table method determine whether the following truth functions are tautologous, contradictory or contingent: (any two 6 (b) Symbolize the following: (Any four) 4 (i) You cannot enter the hall unless you have an ID card. (E, 1) (ii) You will get the job only if you clear the interview. (J, C) (iii) Rahul is intelligent and disciplined. (I, D) (iv) Neither the train nor the flight was delayed. (T, F) (v) Either it will rain or the weather will remain cloudy. (R, C) (vi) You will pass the test if you study diligently. (P, S) (c) Use truth table method to determine the validity / invalidity of the following arguments: (Any One) 4 (iv) Every person is not educated. (Px, Ex) (V) No doctors are careless. (Dx, Cx) (vi) Not all cities are clean. (Cx, Clx) (b) Construct a formal proof of validity of the following. 6 All doctors are professionals. Some nurses are not professionals. Therefore, some nurses are not doctors. (Dx, Px, Nx) (c) Prove the invalidity of the following by the two individual model (any one) - 6 5. (a) Prove the validity/invalidity of the following by Reductio-ad-absurdum method: (any one) 6 (b) Name all the properties found in the following relations (any three) 6 (i) P is of the same age as Q (iii) X is a contemporary of Y. (iv)X is older than Y. (c) Discuss various types of Relations. 4 (d) If the values of A, B, and C are TRUE, X, Y, and Z are FALSE, and the values of P, Q, and R are UNKNOWN, then find out the truth value of the following statements. (Any 3) 3 × 2 = 6 3. (a) Using only the rules of inference and replacement, construct a formal proof of validity of the following. (Any one) 6 (b) Using the Strengthened Rule of Conditional Proof, prove the validity of the following: (Any one) 6 (c) Construct an Indirect Proof of validity of the following: (Any one) 6 4. (a) Symbolize the following sentences by using suggested notations of propositional functions and quantifiers. (Any four) 1.5 × 4 = 6 (i) Some politicians are corrupt. (Px, Cx) (ii) All dogs are loyal animals. (Dx, Lx) (iii) Not all teachers are experienced. (Tx, Ex)