PRACTICE EXERCISES IN PLN
P: Lee studies.
Q: Lee does well.
R: Logic is interesting.
S: Logic is easy.
Symbolize and provide a derivation for a valid argument and a tree or truth-table line for an invalid argument.
1. Lee will study only if logic is easy. She will not do well unless she studies. Logic is not easy. Therefore, Lee will not do well. answer
2. Lee will study if logic is interesting. Unless she studies she will not do well. Logic is interesting. Therefore, Lee will do well. answer
3. Lee will do well only if logic is both easy and interesting. If she studies she will do well. Therefore, if logic is not easy she will not do well. answer
4. Lee will do well if and only if she studies. She will study only if logic is interesting. Logic is interesting only if it is easy, which it is not. Therefore, Lee will not do well. answer
5. Lee must have to study in order to do well. That is because study makes logic interesting, and logic must be interesting for it to be easy. Unless it is easy she won't do well. answer
Fx: x is a logic student
Gx: x is ambitious
Hx: x studies hard
Jx: x is an exercise
Kx: x is easy
Fxy: x does y
a: Bob
b: Carol
6. Bob and Carol are both logic students. All logic students are ambitious. Anyone who is ambitious studies hard. Therefore, Bob and Carol study hard. answer
7. Some logic students are not ambitious. Only ambitious individuals study hard. Therefore, some logic students do not study hard. answer
8. If all the exercises are easy not everyone studies hard. Everyone studies hard, so some of the exercises must not be easy. answer
9. Everyone who studies hard does all the exercises. Carol is not doing all the exercises. Therefore, Carol must not be studying hard. answer
10. Bob does not do any exercises. Only someone doing some of the exercises can be said to be studying hard, so Bob must not be studying hard. answer