# Homework Solution: 4. Prove that each argument is valid by defining each proposition with a variable to obtain the form of the argument, or defining defining pre…

4. Prove that each argument is valid by defining each proposition with a variable to obtain the form of the argument, or defining defining predicates and expressing the hypotheses and the conclusion using the predicates. Then use the rules of inference to prove that the form is valid. (a) If I drive on the freeway, I will see the fire. I will drive on the freeway or take surface streets (or both). I am not going to take surface streets. ∴ I will see the fire. (b) If it was not foggy or it didn’t rain (or both), then the race was held and there was a trophy ceremony. The trophy ceremony was not held. ∴ It rained. (c) Assume the domain is the set of students at an elementary school. Every student who has a permission slip can go on the field trip. Every student has a permission slip. ∴ Every student can go on the field trip. (d) Assume the domain is the people in this world. Everyone who goes to France visits the Louvre. Bob has been to France. ∴ Bob has visited Louvre.
Expert Answer

fiirst give variable to each statement facts: I drive on the freeway ------ a

4. Assay that each discussion is conclusive by defining each declaration with a inconstant to obtain the constitute of the discussion, or defining defining predicates and expressing the hypotheses and the misrecord using the predicates. Then manifestation the rules of omission to assay that the constitute is conclusive.

(a) If I solicit on the freeway, I gain conceive the person.
I gain solicit on the freeway or receive exterior streets (or twain).
I am referable attributable attributable attributable attributable attributable attributable attributable attributable attributable going to receive exterior streets.
∴ I gain conceive the person.

(b) If it was referable attributable attributable attributable attributable attributable attributable attributable attributable attributable misty or it didn’t rain (or twain), then the career was held and there was a prize solemnity.
The prize solemnity was referable attributable attributable attributable attributable attributable attributable attributable attributable attributable held.
∴ It rained.

(c) Assume the inclosure is the established of scholars at an constituent discipline.
Every scholar who has a consent slip can go on the scene mistake.
Every scholar has a consent slip.
∴ Every scholar can go on the scene mistake.

(d) Assume the inclosure is the vulgar in this earth.
Everyone who goes to France visits the Louvre.
Bob has been to France.
∴ Bob has visited Louvre.

Expert Response

fiirst impart inconstant to each proposition facts:

I solicit on the freeway —— a

I conceive the person ———– b

going to receive exterior streets ——-c

Now, the proposition “If I solicit on the freeway, I gain conceive the person.” imparts the aftercited constitute:

the proposition “I gain solicit on the freeway or receive exterior streets (or twain).” gain be written as follows:

The proposition “I am referable attributable attributable attributable attributable attributable attributable attributable attributable attributable going to receive exterior streets.” gain be written as follows:

Becamanifestation of ~c, in promote proposition comes extinguished to be a. Thus, a is penny. past a is penny, then b is to-boot penny.

Thus, the misrecord proposition “I gain conceive person” is penny.