Consider the following: Students who play a lot of video games do not get enough

Question

Consider the following:

Students who play a lot of video games do not get enough sleep. Students who do not get enough sleep do not get good grades. In fact, some students who do not get enough sleep become ill. Jordan is a student who plays a lot of video games. Therefore, Jordan will not get good grades.

Express this argument in symbolic terms: (a) state the propositional functions of one variable, (b) state the premises and the conclusion, and (c) give the steps in the argument (with a reason for each step).

Explanation / Answer

S(x) - x is a student
V(x) - x play video games
L(x) - x gets sleep
I(x) - x gets ill
G(x) - x gets good grades

Premies:
1.S(x) V(x)--> ¬L(x)
2.S(x) ¬L(x) --> I(x)
3.S(x) ¬L(x) --> ¬G(x)

4.S(Jordan)
5.V(Jordan)

Conclusion
¬G(Jordan)

Modes ponens (4,5,1) we get ¬L(Jordan)----(6)

Modes ponens (6,3,4) we get ¬G(Jordan)

Hence proved

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