Question

Several students were asked to formalize the following argument by defining appropriate predicates and then giving the argument as a numbered listed of statements. Each statement was to be labeled either as a premise, or a conclusion from earlier statements, and the argument form used identified. Vegetarians don't eat meat. Bill is a vegetarian. Pork is a kind of meat. Therefore, Bill does not eat pork. Identify the correct answer. Kayaan: the predicates are are: V vegetarian M meat P pork 1. VM (premise) 2. V(Bill) (premise) 3. P M (premise) 4 V(Bill) M(Bill) (universal instantiation of 1.) 5. P(Bill) M(Bill) (universal instantiation of 3.) 6-M(Bill)-P(Bill) (contrapositive of 5.) 7. V(Bil)P(Bill) (hypothetical sylogism from 4. and 6.) 8-P(Bill) (modus ponens from 2. and 7.) Sai: define the predicates Vvegetarian/s M meat Sal:define the predicates V= "vegetarian/s" M "meat P = "pork" E(x,y)"x eats y. E takes as its first input a person and as its second input a food. 1. vx.y (-E(V, M) ) (premise) 2. M P 3.-E(Bill, M) (universal instantiion of 1.) 4.-E(Bill, P) (substituting 2. into 3.) Vihaan: define the predicates V(x) = "x is a vegetarian." B(x) "x is Bill." M(y) y is meat." P(y) y is pork." E(x.y) = "x eats y x is a person, y is a food. 1. Vx.y (V(x) A M(y) E(Xy) (premise) 2. vx (B(x) V(x)) (premise) 3. vy (P(y) M(y) (premise) 4. x, y (B(x)A P(y) 5. x, y (B(x) A P(y)E(x.y)) (universal hypothetical syllogism from 1. and 4) V(x) A M(y)) (universal conjunction from 2. and 3) Ananya: define the predicates V(x) "x is a vegetarian." M(y) "y is meat." E(x.y) "x eats y." = The variablex represents people, the variable y represents foods. 1. vx,y (V(x) A M(y)--E(x.y)) (premise) 2. V(Bill) (premise) 3. M(Pork) (premise) 4. V(Bill) A M(Pork) (conjunction from 2. and 3.) 5. V(Bill) A M(Pork)-E(Bill, Pork) (universal instantiation of 1.) A MV) E(x.y)) (premise) 2. AX (B(x)-V(x)) (premise) 3.Ay (P(y)-M(y) (premise) 4.TX,y (B(x) A P(y) 5. AX, y (B(x) A P(y) V(x) A M(y)) (universal conjunction from 2. and 3) -E(X.y)) (universal hypothetical syllogism from 1. and 4) OAnanya: define the predicates V(x) "x is a vegetarian." M(y) "y is meat." E(x.y) "x eats y." The variable x represents people, the variable y represents foods 1. Vx.y (V(x) A M(y)E(x.y)) (premise) 2. V(Bill) (premise) 3. M(Pork) (premise) 4. V(Bill)A M(Pork) (conjunction from 2. and 3.) 5. V(Bill) A M(Pork)-E(Bill,Pork) (universal instantiation of 1.) 6. -E(Bill,Pork) (modus ponens from 4. and 5.)

Answer 1

The question involves formalizing an argument to prove that Bill, a vegetarian, does not eat pork. It requires using logical structures like universal instantiation, modus ponens, and hypothetical syllogism. Ananya's solution correctly uses these structures to form a valid deductive argument.

Step-by-step explanation:

The question addresses the formalization of an argument involving predicates and logical forms such as universal instantiation, modus ponens, and hypothetical syllogism. The goal is to set up premises that lead to a valid conclusion using deductive reasoning, which demands that if the premises are true, the conclusion necessarily follows.

The key components of the argument include defining what it means to be a vegetarian, what constitutes meat, and what constitutes pork. The student's task was to create valid premises that logically lead to the conclusion that Bill, being a vegetarian, does not eat pork.

Validity depends on the logical structure of the arguments rather than the truth of the premises. This logical structure can contain various forms, such as a disjunctive syllogism, where an either/or statement is resolved, or modus ponens, where the structure is 'If X, then Y; X is true; therefore, Y is true.' Ananya's solution, which ends with modus ponens, formally shows the correct logical sequence to reach the conclusion.