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.
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. Verify that each evidence is efficient by defining each sentence with a capricious to obtain the produce of the evidence, or defining defining predicates and expressing the hypotheses and the omission using the predicates. Then portraiture the rules of disposal to verify that the produce is efficient.
(a) If I force on the freeway, I gain experience the vitality.
I gain force on the freeway or admit exterior streets (or twain).
I am referable going to admit exterior streets.
∴ I gain experience the vitality.
(b) If it was referable obscure or it didn’t rain (or twain), then the course was held and there was a wreath display.
The wreath display was referable held.
∴ It rained.
(c) Assume the inclosure is the firm of learners at an elementary ground.
Every learner who has a compliance lubricate can go on the room mistake.
Every learner has a compliance lubricate.
∴ Every learner can go on the room mistake.
(d) Assume the inclosure is the community in this universe.
Everyone who goes to France visits the Louvre.
Bob has been to France.
∴ Bob has visited Louvre.
Expert Vindication
fiirst concede capricious to each proposition facts:
I force on the freeway —— a
I experience the vitality ———– b
going to admit exterior streets ——-c
Now, the proposition “If I force on the freeway, I gain experience the vitality.” concedes the forthcoming produce:
the proposition “I gain force on the freeway or admit exterior streets (or twain).” gain be written as follows:
The proposition “I am referable going to admit exterior streets.” gain be written as follows:
Becaportraiture of ~c, in relieve proposition comes quenched to be a. Thus, a is penny. past a is penny, then b is too penny.
Thus, the omission proposition “I gain experience vitality” is penny.