Homework Answers
Let A represent for all and E represent there exiists
a) A(x) E (y) F(x) ^ P(x,y)
c) A(x) E(y,z) P(x,y) ^ M(y) ^ P(y,z) ^ not (F(z))
d) A(x, y) E(z) P(z,x) ^ P(z,y) ^ not(x=y)
e) A(x,y) Ez P(x,z) ^ P(y,z)
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6. Consider the predicates M(x), F(x), and P(x, y) in a domain of people. The predicate...
I have have been stuck on this in prolog Design a set of predicates that encode...
I have have been stuck on this in prolog Design a set of predicates that encode genealogical relationships.. • male((XX)) - X is male.. • female((XX)) - X is female.. • parent((XX,,YY)) - X is the parent of Y.. • mother((XX,,YY)) - X is the mother of Y.. • father((XX,,YY)) - X is the father of Y.. • child((XX,,YY)) - X is the child of Y.. • sibling//22 (rreflexive)) • grandparent((XX,,YY)) - X is the grandparent of Y.. • grandmother((XX,,YY))...
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log(2 - 2) (x2 y Question 2. Consider the function f(x, y, (a) What is the maximal domain of f? (Write your answer in set notation.) (b) Find ▽f. (c) Find the tangent hyperplnes Te2)(r, y,z) and Tao2-)f(x, y, z). Find the intersection of these two hyperplanes, and very briefly describe the intersection in words (0,1, 1) and set notation. Confirm that the point (2, 2, 1) is on this level surface, and that Vf(2, 2, 1) is (d) On...
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Logic Programming An important type of programming language is designed to reason using the rules of...
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log(2 - 2) (x2 y Question 2. Consider the function f(x, y, (a) What is the maximal domain of f? (Write your answer in set notation.) (b) Find ▽f. (c) Find the tangent hyperplnes Te2)(r, y,z) and Tao2-)f(x, y, z). Find the intersection of these two hyperplanes, and very briefly describe the intersection in words (0,1, 1) and set notation. Confirm that the point (2, 2, 1) is on this level surface, and that Vf(2, 2, 1) is (d) On...
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2, M = 〈D, δ〉 is a model for a first-order language with a unary predicate...
log(2 - 2) Consider the function f(x, y,z) (a) What is the maximal domain off? (Write your answer in set notation.) Find ▽f. (b) Find the tangent hyperplanes Ta2.1,f(r, y, 2) and To-ef(r, y, 2). Find the intersection (c) On (z, y, z)-axes, draw arrows representing the vector field F = Vf at the points (1,0,1), (d) Find the level set of f which has value ("height") wo 0, and describe it in words and of these two hyperplanes, and...
Use the rules of deduction in the Predicate Calculus (but avoiding derived rules) to find formal proofs for the following sequents: (a) x) F)~(Vx)~ F(x) (b) (Vz) ~ F(x) B) F() (3x)(G(z) Л (Vy) (F(y) H(y, z))) (e)
Use the rules of deduction in the Predicate Calculus (but avoiding derived rules) to find formal proofs for the following sequents: (a) x) F)~(Vx)~ F(x) (b) (Vz) ~ F(x) B) F() (3x)(G(z) Л (Vy) (F(y) H(y, z))) (e)
2. Consider the surface -v 9-2r2-r : f(x, y) z (a) What is the domain and range of f? (b) Sketch the level curves for 2-f(r,y) -0,-3,-2V2,-v5 (c) Sketch the cross sections of the surface in the r-2 plane and in the y-z plane (d) Find any z, y and z intercepts Use the above information to identify and sketch the surface.
2. Consider the surface -v 9-2r2-r : f(x, y) z (a) What is the domain and range of...
3. Suppose that (M, ρ) is a compact metric space and f : (M, p)-+ (M,p) is a function such that (Vz, y E M) ρ (z, y) ρ (f (x), f (y)). a. Let x E (M, ρ) and consider the sequence of points {f(n) (X)}n 1 . (Remember: fn) denotes the composition of f with itself, n times, so for each n, f+() rn, k E N) such that ρ (f(m) (x) ,f(n +k) (r)) < ε ....
Logic Programming An important type of programming language is designed to reason using the rules of predicate logic. Prolog (from Programming in Logic), developed in the 1970s by computer scientists working in the area of artificial intelligence, is an example of such a language. Prolog programs include a set of declarations consisting of two types of statements, Prolog facts and Prolog rules. Prolog facts define predicates by specifying the elements that satisfy these predicates. Prolog rules are used to define...
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