------------------------------------------- Define the following propositions: c

Question

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Define the following propositions:

c: I will return to college.

j: I will get a job.

Translate the following English sentences into logical expressions using the definitions above:

(a)

Not getting a job is a sufficient condition for me to return to college.

(b)

If I return to college, then I won't get a job.

(c)

I am not getting a job, but I am still not returning to college.

(d)

I will return to college only if I won't get a job.

(e)

There's no way I am returning to college.

(f)

I will get a job and return to college.

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Define the following propositions:

s: a person is a senior

y: a person is at least 17 years of age

p: a person is allowed to park in the school parking lot

Express each of the following English sentences with a logical expression:

(a)

A person is allowed to park in the school parking lot only if they are a senior and at least seventeen years of age.

(b)

A person can park in the school parking lot if they are a senior or at least seventeen years of age.

(c)

Being 17 years of age is a necessary condition for being able to park in the school parking lot.

(d)

A person can park in the school parking lot if and only if the person is a senior and at least 17 years of age.

(e)

Being able to park in the school parking lot implies that the person is either a senior or at least 17 years old.

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For each table, give a logical expression whose truth table is the same as the one given.

(a)

(b)

Explanation / Answer

Define the following propositions:

c: I will return to college.

j: I will get a job.

Translate the following English sentences into logical expressions using the definitions above:

(a)

Not getting a job is a sufficient condition for me to return to college.
¬j c

(b)

If I return to college, then I won't get a job.
c ¬j

(c)

I am not getting a job, but I am still not returning to college.
¬j ¬c

(d)

I will return to college only if I won't get a job.
c ¬j

(e)

There's no way I am returning to college.
¬c

(f)

I will get a job and return to college.
j c

NOTE that we cannot represent tense using logic.

If you need any explanation, please comment below. I shall try my best to resolve all your issues.

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