Use the predicate symbols shown. Some elephants are afraid of all mice. Some mice are small. Therefore there is an elephant that is afraid of something small. E(x), M(x), A(x, y), S(x)

Consider the predicates Martian (x): x is a MartianisGreen(x): x is green Use equivalence laws of first-order logic to identify the expression that is logically equivalent to ∀x (Martian(x) ˄ isGreen(x)) Group of answer choices ∃x (Martian(x)) ˅ ∃x (isGreen(x)) ∃x (¬Martian(x)) ˄ ∃x (¬isGreen(x)) ∀x (Martian(x)) ˄ ∀x (isGreen(x)) ∀x (¬Martian(x)) ˄ ∀x (¬isGreen(x))

Answer (c)

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 don’t do the homework, you won’t pass the final. Curly did not do the homework. Therefore Curly did not pass the final.   If you do the homework you will pass the final. If you pass the fi- nal you will pass the course. Larry did the homework. Therefore Larry will pass the course. Curly, Moe and Larry are stooges. Curly did his homework. Therefore a stooge did his homework.

In the context of Propositional Logic, using letters to denote sentences components, translate the following compound sentences into symbolic notation. In the translation indicate clearly the meaning of each propositional letter: A. Roses are red and violets are blue. B. Whenever violets are blue, roses are red and sugar is sweet. C. Roses are red only if the violets are not blue and the sugar is sour. D. Roses are red and if sugar is sour then violets are not blue or sugar is sweet

Please Help with the question below: Suppose you are given some facts in First-Order Logics: a) Andi is a professor b) All professors are people. c) Ani is the dean. d) All Deans are professors. e) All professors consider the dean a friend or don’t know him. f) Everyone is a friend of someone. g) People only criticize people that are not their friends. h) Andi criticized Ani. Prove that: Ani is not Andi’s friend.

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.

PLEASE TYPE Exercise 1.7.10: Determining whether a quantified logical statement is true, part 2. A student club holds a meeting. The predicate M(x) denotes whether person x came to the meeting on time. The predicate O(x) refers to whether person x is an officer of the club. The predicate D(x) indicates whether person x has paid his or her club dues. The domain is the set of all members of the club. The names of the members and their truth values for each of the predicates is given in the following table. Indicate whether each expression is true or false. If a universal statement is not true, give a counterexample. If an existential statement is true, give an example. Name M(x) O(x) D(x) Hillary T F T Bernie F T F Donald F T F Jeb F T T Carly F T F     (i) ∃x (O(x) → M(x)) (j) ∃x (M(x) ∧ O(x) ∧ D(x))

Using the predicate symbols shown and the appropriate quantifiers, write each English language statement as a predicate wff. (The domain is the whole world.) B(x): x is a bee. F(x): x is a flower. L(x, y): x loves y All bees love all flowers which one of these answer choices a. (∀x)(B(x) → [(∃y)(F(y) ∧ L(x, y)] b. (∀x)(B(x) → [(∀y)(F(y) ∧ L(x, y)] c. (∀x)(B(x) → [(∀y)(F(y) → L(x, y)] d. (∀x)(B(x) ∧ [(∃y)(F(y) → L(x, y)]

The predicate for the following proposition – “Harry plays football” – can be written as:   a.   (Plays,football,P)   b.   football_P(Plays)   c.   Plays(football,p)   d.   P_(football)(Plays)