Consider the following statements (the domain of x is all people):...

Question

# Consider the following statements (the domain of x is all people):...

Consider the following statements (the domain of x is all people):
(a) Each student in the class has a computer.
(b) Everyone with a computer can program.
(c) Mary is a student in the class.
(d) Therefore, Mary can program.
Let S(x) mean "x is a student in the class", C(x) mean "x has a computer", and P(x) mean "x
can program." You will first translate the statements into logical expressions (2 pts). Then, show
the conclusion (d) can be drawn from the prior statements (a-c) (6 pts). Justify each step of the
argument.

Let w = "I work on CS for 10 hours a week",
g = "I graduate in four years",
c = "I will complete the CS courses", and
p = "I procrastinate."
Use the same propositional variables of problem 2 and the rules of inference to show

Let w = "I work on CS for 10 hours a week",
g = "I graduate in four years",
c = "I will complete the CS courses", and
p = "I procrastinate."
the hypotheses imply the conclusion:
•"If I work on CS for 10 hours a week and I don't procrastinate, then I will complete the CS
courses",
•"I will not graduate in four years and I worked on CS for 10 hours a week.", and
•"If I complete the CS courses, then I graduate in four years."
Conclusion: "I procrastinated."
First, translate the hypotheses and conclusion in to logical statements (4 points). Then, show the
valid argument (8 points).

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## Step-by-step explanation

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