# Answered Essay: 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.

fiirst give variable to each statement facts:

I drive on the freeway —— a

I see the fire ———– b

going to take surface streets ——-c

Now, the statement “If I drive on the freeway, I will see the fire.” gives the following form:

the statement “I will drive on the freeway or take surface streets (or both).” will be written as follows:

The statement “I am not going to take surface streets.” will be written as follows:

Because of ~c, in second statement comes out to be a. Thus, a is true. since a is true, then b is also true.

Thus, the conclusion statement “I will see fire” is true.

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