4. Given the predicates male(x), female(x), parent(x, y) (x is a parent of y), define the following predicates in terms of male, female, parent, or other pred- icates defined from these three predicates, in first-order logic: (a) father(x, y): x is the father of y. (b) mother(x, y): x is the mother of y. (c) ancesotor(x, y): x is an ancestor of y.

4. Given the predicates male(x), female(x), parent(x, y) (x is a parent of y), define the following predicates in terms of male, female, parent, or other pred- icates defined from these three predicates, in first-order logic: (a) father(x, y): x is the father of y. (b) mother(x, y): x is the mother of y. (c) ancesotor(x, y): x is an ancestor of y.

Name: 4. Given the predicates male(x), female(x), parent(x, y) (x is a pare
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: 4. Given the predicates male(x), female(x), parent(x, y) (x is a parent of y),define the following predicates in terms of male, female, parent, or other pred-icates defined from these three predicates, in first-order logic:(a) father(x, y): x is the

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Q4. Simplify the following sentences in predicate logic so that all the negation symbols are directly in front of a predicate. (For example, Vr (-0(1)) (-E(r))) is simplified, because the negation symbols are directly in front of the predicates O and E. However, Vr -(P(x) V E(x)) is not simplified.) (i) -(3r (P(x) V (E(x) → S(x)))) (ii) -(Vz (E(r) A (P(x) →¬(3y G(x, y))) Q5. Write a sentence in predicate logic (using the same predicates as above) which is true when the domain is the class of positive integers (1, 2, 3, ...), but is false when the domain is the class of all integers (...,-2, -1,0, 1, 2, ...). (You do not need to explain your answer.)
please explain in details....
27. Translate each of these statements into logical expres- sions in three different ways by varying the domain and by using predicates with one and with two variables. a) A student in your school has lived in Vietnam. b) There is a student in your school who cannot speak Hindi. c) A student in your school knows Java, Prolog, and C++. d) Everyone in your class enjoys Thai food. e) Someone in your class does not play hockey.
2. Given a predicate logic sentence: E: if (for all x)p(x, f(y)) then p(a, f(y)) Show that & is valid.
Dear expert don't Use chat gpt
Let Q(x, y) be the predicate " has sent y an email." Which of the following expresses the statement "Everyone has emailed somebody. OxVy Q(x, y) Vy Q(x, y) OxVy Q(y, x) Vy Qy, x)
6) In the domain of all computer science majors, let G(x) be the predicate "x is required to take geometry". Write the following statements in the symbols of predicate logic. a) There is a computer science major that is not required to take geometry. b) There is no computer science major that is required to take geometry. c) Every computer major is not required to take geometry. d) All computer science majors are required to take geometry.
3
please solve question A and B
Q.6 Convert the following sentence to conjunctive normal form (CNF). (A B) =C (Hint: Study Conjunctive normal form (CNF) and Standard logical equivalences)
Q7. Let z and y be propositional variables, and let P₁: zvy Pr:x A-y Ps: yr C:y Answer the following three questions, in order: • Is the argument (P₁ P₂^ P3) → C valid? • Is the set {P₁, P2, P3} consistent? • Are P₂ and-P3 logically equivalent? A. Yes, no, yes. B. No, yes, yes. C. No, yes, no. D. Yes, no, no. E. Yes, yes, yes. F. No, no, yes. G. none of the above.
Q7: Translate the following statement into English, where R(x) is "x is a rabbit" and H (x) is "x hops" and the domain consists of all animals. • 3x(R(x) → H (x)) Q8: Translate in two ways the following statement into logical expressions using predicates, quantifiers, and logical connectives. First, let the domain consist of the students in your class and second, let it consist of all people. Everyone in your class has a cellular phone. Q9: (* Let P (x, y) be the statement "Student x has taken class y," where the domain for x consists of all students in your class and for y consists of all computer science courses at your school. Express the following quantification in English. 3XVYP (x, y)