Your familiar \"un-quantified\" rules of inference (modus ponens, disjunctive sy

Question

Your familiar "un-quantified" rules of inference (modus ponens, disjunctive syllogism, etc), The quantified versions of Modus Ponens/Tollens and Hypothetical Syllogism, all of which are presented in chapter 3.4 of our textbook and Axioms of logical equivalence (associativity, double negation, etc) show that the proofs depicted in table 4 are valid. Note that we are not asking you to use truth tables of any kind. We are asking you to use quantified ("universal", in the terminology of Epp), rules of inference to deduce the conclusions themselves. For every step of the derivation, document which rule or axiom of equivalence you are using. We assume some well-defined domain D. Note that the last rule contains 3 (three) premises, the third of which is an existentially quantified disjunction.

Explanation / Answer

Answer:

1. The universal quantifier is Modus ponnens

Example : All men are mortalSocrates is a man.

consequently Socrates is morta

l at this time let X implies universal statement

R(x)= All men P(x) =All mortal

Let a be the domain of X where a is considered as Socrates

at this time q(a) is scocrates is men and P(a)= socrates being mortal.

2.The universal quantifier is modus tollens

Example : All good drivers are attentive

people who drunk are not attentive

therefore all people who drunk are not good drivers

From the above example R(x) =people who are good drivers and

P(x)= all are attentive

for a particular a belongs to X where q(a) is a set of people who are drunk

negation~ P(a) egationwedge q(a) =all people drunk are not attentive

therefore ~R(a) implies that people who are drunk are not good drivers

3.Example: If it rains,you take umbrella

If is it cloudy,it rains

neither Anil is carrying umbrella nor it is raining

therefore it is not cloudy

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.