Homework Answers
4)answer)
∃x (x+2=2)
here this is satisfiable because for value x=0 above statement is true.
5)answer)given ~∃y∀x A(x,y) and ∀y∃x ~A(x,y) don't have same value
apply negation for ∀y∃x ~A(x,y) then
~(∀y∃x ~A(x,y))=∃y∀x A(x,y)
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4. Provide an example of a satisfiable first-order logic formula. Show why it's satisfiable. 5. Prove...
consider this first- order logic formula: ∃x P(a,x) --> ∀y P(b,y) and its interpretation which is:...
consider this first- order logic formula: ∃x P(a,x) --> ∀y P(b,y) and its interpretation which is: Domain D = {1,2,3}, P{(1,1), (1,2), (1,3), (2,3), (3,1)}, a=1, b=3. is it valid, satisfiable, or contradictory? why?
consider this first- order logic formula: ∃x P(a,x) --> ∀y P(b,y) and its interpretation which is:...
consider this first- order logic formula: ∃x P(a,x) --> ∀y P(b,y) and its interpretation which is: Domain D = {1,2,3}, P{(1,1), (1,2), (1,3), (2,3), (3,1)}, a=1, b=3. is it valid, satisfiable, or contradictory? why?
UIC 5. (20 pt.) Use the laws of propositional logic to prove that the following compound...
UIC 5. (20 pt.) Use the laws of propositional logic to prove that the following compound propositions are tautologies. a. (5 pt.) (p^ q) → (q V r) b. (5 pt) P)Ag)- Vg)A(A-r)- c. (10 pt.) Additional Topics: Satisfiability (10 pt.) A compound proposition is said to be satisfiable if there is an assignment of truth values to its variables that makes it true. For example. p ^ q is true when p = T and q = T;thus, pAqissatsfiable....
(b) Using the Davis-Putnam-Logemann-Loveland (DPLL) algorithm, determine whether the following formula is satisfiable. Show each step. [3 marks] (c) Give an example of a conjunctive normal form (...
(b) Using the Davis-Putnam-Logemann-Loveland (DPLL) algorithm, determine whether the following formula is satisfiable. Show each step. [3 marks] (c) Give an example of a conjunctive normal form (CNF) formula where the pure literal rule can be applied, but the unit propagation rule cannot. The formula must have at least 3 clauses. [3 marks
(b) Using the Davis-Putnam-Logemann-Loveland (DPLL) algorithm, determine whether the following formula is satisfiable. Show each step. [3 marks] (c) Give an example of a conjunctive normal form...
Suppose that we add a new quantifier called exists unique to first- (d) order logic, using the symbol 3! to represent it. It means that there is exactly one element of the universe that satisfies...
Suppose that we add a new quantifier called exists unique to first- (d) order logic, using the symbol 3! to represent it. It means that there is exactly one element of the universe that satisfies the subsequent formula. In this question, variables will range over the universe of numbers. [1 mark] (0) Is 3!x. x + x 2 valid? Why? Give an example of a valid formula that uses the quantifier, and an example of an unsatisfiable one. Both must...
X(f(y) = x))) (Hint: the rules about functions in first order logic apply to functions in set the...
x(f(y) = x))) (Hint: the rules about functions in first order logic apply to functions in set theory also) 3. Prove that for any set X, the function f : X → P(X) where f(x)-{y E X : yメx} is an injection.
x(f(y) = x))) (Hint: the rules about functions in first order logic apply to functions in set theory also) 3. Prove that for any set X, the function f : X → P(X) where f(x)-{y E X :...
Logic Quiz 5 Show these two compound propositions to be true or false 1. Rome is the capital of I...
Logic Quiz 5 Show these two compound propositions to be true or false 1. Rome is the capital of Italy or Paris is the capital of England 2. If London is not the capital of Italy then Stockholm is the capital of Italy 3. 4. Given that A, B, C, are true statements and X, Y, Z are false, show that the following two statements (a and b) are true or false (Xv Y)AXvZ) a) b) I(B C)v (CAB) Prove...
Logic problem： Symbolize in the language of First-Order Logic, using the dictionary provided below.
Logic problem：
Symbolize in the language of First-Order Logic, using the
dictionary provided below.
Symbolize in the language of First-Order Logic, using the dictionary provided below. DICTIONARY · m = MITS (The Man In The Street) . w= wITS (The Woman in the Street) · 1=Logic · Lx = x is a logician . PX-x is a pacifist Mx-x is a man . .Wx-x is a woman Rxy-x respects y Lxy = x loves y Sxy x is smarter than...
First-Order Logic Knowledge Representation Exercise Set #3 Translate each of the following English sentences into first-order...
First-Order Logic Knowledge Representation Exercise Set #3 Translate each of the following English sentences into first-order logic, using only the following constants and predicates... Constants: Joe- a person named Joe McCartney-a person named Paul McCartn Gershwin-a person named George Gershwin BHoliday- a person named Billie Holiday EleanorRigby- a song entitled "Eleanor Rigby" TheManILove-a song entitled "The Man I Love" Revolver- the music album entitled "Revolver" ey Predicates: CopyOffx,y) compact disk x is a copy of music album y ·Owns(x,y) ....
If a statement is true, prove it. If not, give an example of why it is...
If a statement is true, prove it. If not, give an example of
why it is false. Please neatly and carefully show all necessary
work.
4.If f :RR is such that both (0,0) and f(0.v) are continuous at (0,0), then f(x,y) is continuous at (0,0). 5. If f posses all of its directional derivatives at (a, b), then / is differentiable at (a,b). 6. If fr and fy both exist at (a, b), then all other directional derivatives exist at...
UIC 5. (20 pt.) Use the laws of propositional logic to prove that the following compound propositions are tautologies. a. (5 pt.) (p^ q) → (q V r) b. (5 pt) P)Ag)- Vg)A(A-r)- c. (10 pt.) Additional Topics: Satisfiability (10 pt.) A compound proposition is said to be satisfiable if there is an assignment of truth values to its variables that makes it true. For example. p ^ q is true when p = T and q = T;thus, pAqissatsfiable....
(b) Using the Davis-Putnam-Logemann-Loveland (DPLL) algorithm, determine whether the following formula is satisfiable. Show each step. [3 marks] (c) Give an example of a conjunctive normal form (CNF) formula where the pure literal rule can be applied, but the unit propagation rule cannot. The formula must have at least 3 clauses. [3 marks
(b) Using the Davis-Putnam-Logemann-Loveland (DPLL) algorithm, determine whether the following formula is satisfiable. Show each step. [3 marks] (c) Give an example of a conjunctive normal form...
Suppose that we add a new quantifier called exists unique to first- (d) order logic, using the symbol 3! to represent it. It means that there is exactly one element of the universe that satisfies the subsequent formula. In this question, variables will range over the universe of numbers. [1 mark] (0) Is 3!x. x + x 2 valid? Why? Give an example of a valid formula that uses the quantifier, and an example of an unsatisfiable one. Both must...
x(f(y) = x))) (Hint: the rules about functions in first order logic apply to functions in set theory also) 3. Prove that for any set X, the function f : X → P(X) where f(x)-{y E X : yメx} is an injection.
x(f(y) = x))) (Hint: the rules about functions in first order logic apply to functions in set theory also) 3. Prove that for any set X, the function f : X → P(X) where f(x)-{y E X :...
Logic Quiz 5 Show these two compound propositions to be true or false 1. Rome is the capital of Italy or Paris is the capital of England 2. If London is not the capital of Italy then Stockholm is the capital of Italy 3. 4. Given that A, B, C, are true statements and X, Y, Z are false, show that the following two statements (a and b) are true or false (Xv Y)AXvZ) a) b) I(B C)v (CAB) Prove...
Logic problem：
Symbolize in the language of First-Order Logic, using the
dictionary provided below.
Symbolize in the language of First-Order Logic, using the dictionary provided below. DICTIONARY · m = MITS (The Man In The Street) . w= wITS (The Woman in the Street) · 1=Logic · Lx = x is a logician . PX-x is a pacifist Mx-x is a man . .Wx-x is a woman Rxy-x respects y Lxy = x loves y Sxy x is smarter than...
First-Order Logic Knowledge Representation Exercise Set #3 Translate each of the following English sentences into first-order logic, using only the following constants and predicates... Constants: Joe- a person named Joe McCartney-a person named Paul McCartn Gershwin-a person named George Gershwin BHoliday- a person named Billie Holiday EleanorRigby- a song entitled "Eleanor Rigby" TheManILove-a song entitled "The Man I Love" Revolver- the music album entitled "Revolver" ey Predicates: CopyOffx,y) compact disk x is a copy of music album y ·Owns(x,y) ....
If a statement is true, prove it. If not, give an example of
why it is false. Please neatly and carefully show all necessary
work.
4.If f :RR is such that both (0,0) and f(0.v) are continuous at (0,0), then f(x,y) is continuous at (0,0). 5. If f posses all of its directional derivatives at (a, b), then / is differentiable at (a,b). 6. If fr and fy both exist at (a, b), then all other directional derivatives exist at...
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