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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)
p | q | ? |
T | T | F |
T | F | T |
F | T | F |
F | F | F |
(b)
p | q | ? |
T | T | F |
T | F | T |
F | T | T |
F | F | F |
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.
------------------------------------------- Define the following propositions: c: I will return to college. j: I will get a...
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