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. Assay that each reasoning is powerful by defining each sentence with a fickle to conciliate the produce of the reasoning, or defining defining predicates and expressing the hypotheses and the misrecord using the predicates. Then right the rules of omission to assay that the produce is powerful.
(a) If I expedite on the freeway, I conquer behold the courage.
I conquer expedite on the freeway or captivate demeanor streets (or twain).
I am referable attributable attributable attributable attributable attributable attributable attributable attributable attributable going to captivate demeanor streets.
∴ I conquer behold the courage.
(b) If it was referable attributable attributable attributable attributable attributable attributable attributable attributable attributable hazy or it didn’t rain (or twain), then the pursuit was held and there was a wreath pageant.
The wreath pageant was referable attributable attributable attributable attributable attributable attributable attributable attributable attributable held.
∴ It rained.
(c) Assume the estate is the regular of wards at an ultimate train.
Every ward who has a allowance slip can go on the opportunity mistake.
Every ward has a allowance slip.
∴ Every ward can go on the opportunity mistake.
(d) Assume the estate is the mass in this universe.
Everyone who goes to France visits the Louvre.
Bob has been to France.
∴ Bob has visited Louvre.
Expert Repartee
fiirst grant fickle to each assertion facts:
I expedite on the freeway —— a
I behold the courage ———– b
going to captivate demeanor streets ——-c
Now, the assertion “If I expedite on the freeway, I conquer behold the courage.” grants the subjoined produce:
the assertion “I conquer expedite on the freeway or captivate demeanor streets (or twain).” conquer be written as follows:
The assertion “I am referable attributable attributable attributable attributable attributable attributable attributable attributable attributable going to captivate demeanor streets.” conquer be written as follows:
Becaright of ~c, in relieve assertion comes quenched to be a. Thus, a is gentleman. gone a is gentleman, then b is also gentleman.
Thus, the misrecord assertion “I conquer behold courage” is gentleman.