Using the following predicates, any needed logical operators, and quantifiers if needed, translate the following English statements . Assume the domain of x is all students and the domain of y is all states in US. B(x, y): Person x has been to state y. L(x, y): Person x likes state y. a. No one has been to every state in US. d. Alice has been to every state that Bob has been to. e. There is no state that both Alice and Bob have been to.

Need the right answer among choices and also an explanation of the answer.

Using the predicate symbols shown and appropriate quantifiers, write each English language statement as a predicate wff. (The domain is the whole world.) D(x): x is a day S(x): x is sunny R(x): x is rainy M: Monday T: Tuesday 1. All animals are dogs.  2.Some animals are not cats. 3.Every animal that is a dog is not a cat. 4.Some animals are dogs and cats. 5.No animal is both a dog and a cat. 6. An animal is always a dog only if it is a cat. 7.No animals are dogs. 8.Meg is a cat; all animals are cats. 9.Meg and Alex are both cats. 10.If one animal is a cat, then every animal will be a cat.

Write the following English statements using the following predicates, anyneeded logical operators, and quantifiers if needed. Assume the domain of x is all students and thedomain of y is all states in US.B(x, y): Person x has been to state y. L(x, y): Person x likes state y. a. No one has been to every state in US.d. Alice has been to every state that Bob has been to.e. There is no state that both Alice and Bob have been to.

Exercise 5 - A Use only two logical symbols, C and G to transform the following English sentences to logical propositions. Use the following connective abbreviation (symbols) Connective Symbol (abbreviation) OR V AND NOT Implication Equivalence => Sentence Logical proposition 1) Al makes easy education or industry 2) Al makes easy education but also industry 3) Al makes easy education and makes easy or not industry 4) Al makes easy education if and only if it makes it difficult Note: Al: Artificial Intelligence

Convert each of the following argu- ments into formal statements, e.g., define sentences existentially and/or universally quantified statements. Then determine which rules of logic have been applied and explain whether or not they have been ap- plied correctly. if you do the homework you will pass the final. Somebody did not pass the final. Therefore somebody did not not do the homework. If you do the homework you will pass the final. Curly did not do the homework. Therefore Curly will not pass the final. If you don’t do the homework, you won’t pass the final. Moe did the homework. Therefore Moe passed the final.

I will thumbs up if you answer all. please convert FOL to CNF  Convert each of the following English statements into a single first-order logic sentence using the following constants and predicates. •Constants: Apples, Oranges, Chess, Go, John, Mary. •Predicates: oLikes(x,y): person x likes food y oPlays(x,y): person x plays game y a.If a personlikesApples, then they play chess. b.If a person likesOranges, then they play Go. c.A person likesApples or Oranges, but not both. d.John likes apples. e.Mary does not like anything that John likes. and then: Convert each of the first-order logic sentences in Problem 2to conjunctive normal form (CNF). There is no need to show intermediate steps. Assign each clause number: C1, C2, etc.

in discrete data structure Using predicate logic, prove that each argument in Exercise 42 is valid. Use the predicate symbols shown. Customized) There is some car that is faster than anything. Anything that is faster than anything else consumes more gasoline than anything else does. Therefore, there is a car that consumes more gasoline than anything. C(x): x is a car  F(x,y): x is faster than y G(x,y): x consumes more gasoline than anything

Let the domain be the set of all animals. Define the following predicates: A(x) : x can add. • W(x) : x can waltz. • D(x) : x is a dog. • C(x) : x is a cat. Translate each of the following logical expressions into English. 1. Vx(D(x) → (A(x) V W(x)). 2. Ex(C(x) A ¬A(x) ^ W(x)) 3. -3x(D(x) ^ A(x)) 4. Vx((D(x) V C(x)). → W(x))

Mathematical Logic. First-order or predicate logic. For each of the following relations, give a formula that defines it in (N;+,∙). The language has equality and has the parameters ∀,+ and ∙. a) {0} b) {1} c) {〈m,n〉| n is the successor of m in N} d) {〈m,n〉| n<n in N} Please be as clear as possible. Thank you.