- 5 Let P M N Be The Statement M Divides N Where The Universe Of Discourse For Both The Variables Is The Set Of Positi 1 (80.17 KiB) Viewed 53 times
5. Let P(m,n) be the statement "m divides n" where the Universe of discourse for both the variables is the set of positive integers. Determine the truth values of the following propositions. (i) 3m Vn P(m,n) (ii) Vn P(1,n) (iii) Vm Vn P(m,n) A. (i)-True; (ii)-True; (iii)-False C. (i)-False; (ii)-False; (iii)-False B. (i)-True; (ii)-False; (iii)-False D. (i)-True; (ii)-True; (iii)-True 6. Consider the compound propositions given below as: (i) pv-(p^q) (ii) (p^-q) V-(p^g) Which of the above propositions are tautologies (always true)? (iii) p^ (qVr) A. (i) and (iii) B. (ii) and (iii) C. only (i) D. (i), (ii) and (iii) 7. Forward chaining systems are A. Data driven, Data driven B. Goal driven, Data driven C. Data driven, Goal driven D. Goal driven, Goal driven 8. A horn clause is......... ........ A. A clause in which no variables occur in the expression B. A clause that has at least one negative literal C. A disjunction of a number of literals D. A clause that has at most one positive literal 9. Reasoning strategies used in expert systems include: A. Forward chaining, backward chaining and problem reduction B. Forward chaining, backward chaining and boundary mutation C. Forward chaining, backward chaining and back propagation D. Backward chaining, problem reduction and boundary mutation 10. Give a compound proposition involving propositions p, q and r that is true when exactly two of p, q and r are true and is false otherwise. A. (pVgr) V (pvq^r)^(-p^q^r) B. (p^qVr)^(p^q^r) V (p^q^r) C. (p^g^-r) V (PV-q ^r) V (p^q^r) D. (pVT Ag) V (p^g^r) V(p^g^r) 11. Which of the following is a correct predicate logic statement for "Every Natural number has one successor"? A. Vx3y (succ(x,y)A (3 z succ(x,z)→ equal(y,z))) B. V x3y (succ(x,y)v (3 z succ(x,z)→ equal(y,z))) C. 3y Vx (succ(x,y)A (3 z succ(x,z)→ equal(y,z))) D. Vx3y succ(x,y) 12. The preposition (p→q) ^ (-q V p) is equivalent to: A. q→P B. p q C. (q→p) ^ (p→g) D. (p g) V (q→ p) Page 2 whereas backward chaining systems are