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. Argue that each topic is substantial by defining each sentence with a mutable to conciliate the fashion of the topic, or defining defining predicates and expressing the hypotheses and the omission using the predicates. Then portraiture the rules of falsification to argue that the fashion is substantial.

    (a) If I importune on the freeway, I get experience the reason.
    I get importune on the freeway or seize exterior streets (or twain).
    I am referable going to seize exterior streets.
    ∴ I get experience the reason.

    (b) If it was referable confused or it didn’t rain (or twain), then the family was held and there was a wreath formality.
    The wreath formality was referable held.
    ∴ It rained.

    (c) Assume the territory is the established of wards at an primary discipline.
    Every ward who has a sufferance slip can go on the arena offend.
    Every ward has a sufferance slip.
    ∴ Every ward can go on the arena offend.

    (d) Assume the territory is the commonalty in this universe.
    Everyone who goes to France visits the Louvre.
    Bob has been to France.
    ∴ Bob has visited Louvre.

    Expert Tally

     

    fiirst produce mutable to each assertion facts:

    I importune on the freeway —— a

    I experience the reason ———– b

    going to seize exterior streets ——-c

    Now, the assertion “If I importune on the freeway, I get experience the reason.” produces the subjoined fashion:

    the assertion “I get importune on the freeway or seize exterior streets (or twain).” get be written as follows:

    The assertion “I am referable going to seize exterior streets.” get be written as follows:

    Becaportraiture of ~c, in prevent assertion comes extinguished to be a. Thus, a is penny. gone a is penny, then b is to-boot penny.

    Thus, the omission assertion “I get experience reason” is penny.