# MFCS MATHEMATICS

May 19th, 2015
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1) (a) Determine the truth value of each of the following statements i. 6 + 2 = 7 and 4 + 4 = 8. ii. four is even. iii. 4 + 3 = 7 and 6 + 2 = 8. (b) Write each of the following statements in symbolic form i. Anil & Sunil are rich. ii. Neither Ramu nor Raju is poor. iii. It is not true that Ravi & Raju are both rich.

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SUB: MFCS FACULTY: S. JAGADESH BABUUNIT 1:1) (a) Determine the truth value of each of the following statements i. 6 + 2 = 7 and 4 + 4 = 8. ii. four is even. iii. 4 + 3 = 7 and 6 + 2 = 8. (b) Write each of the following statements in symbolic form i. Anil & Sunil are rich. ii. Neither Ramu nor Raju is poor. iii. It is not true that Ravi & Raju are both rich. (c) Write a short note on normal forms2) (a) Prove that (P Q)V R ((P V Q)R) is a contradiction. (b) Obtain PDNF and PCNF of the following formula (PVQ) (P Q)3) (a) Show the following implication without constructing the truth table. i. (P Q) Q (PVQ) ii. P Q P (PQ) (b) Show that the proposition PQ and (PVQ) (P) (Q) are contradiction4) (a) If P is true, Q is false and R is true, then find the truth value of ((P Q) R)V (P V R) without constructing the truth table. (b) Find the disjunctive normal form of P V (P (QV (Q R))). ( c) Show that the following statements is a

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