2023 Fall Phil 111 Extra Credit Assignment - Rules of Replacement Pt 2
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Dec 6, 2023
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Philosophy 110
Extra Credit Assignment: Rules of Replacement, Part 2
Fall 2023
Deadline for Submission: Sunday, 11/19/23, by 11:59 pm.
This assignment is optional, for up to 40 extra credit course points. (Your grade will not be
harmed if you do not complete this assignment.) To receive points, the answers must be
correct. The assignment covers the extra credit material posted in the Week 12 course
module.
Part 1: Use the first 16 rules of inference (the 8 rules of implication and first 8 rules of
replacement) to provide logical proofs with line-by-line justifications for the following
arguments.
The logical operators used must be the ones we are using in this class; no other operators will
be accepted. The method used to solve each problem must be the method we are using in this
class; no other methods or steps will be accepted.
1.
1. G > H
2. H > I
/~I > ~G
2.
1. X > Y
2. Y > Z
/~X v Z
3.
1. ~A > B
2. B > A
/A
4.
1. (E > F) & (E > G)
2. ~F v ~G
/~E
Part 2: Translate the following arguments into symbolic form and use the first 16 rules of
inference (the 8 rules of implication and first 8 rules of replacement) to provide logical proofs
with line-by-line justifications. The letters to be used for the simple statements are given in
parentheses after each exercise. Use the letters in the order in which they are used.
5.
If Russia invades Ukraine, then Finland joins NATO. Either Finland does not join NATO or
Sweden joins NATO. Therefore, if Russia invades Ukraine, then Sweden joins NATO. (R, F, S)
Part 3: Use the 18 rules of inference (the 8 rules of implication and the 10 rules of replacement)
to provide logical proofs with line-by-line justifications for the following arguments.
The logical operators used must be the ones we are using in this class; no other operators will
be accepted. The method used to solve each problem must be the method we are using in this
class; no other methods or steps will be accepted.
6.
1. (P & O) > N
2. P
/~N > ~O
7.
1. (T v ~U) > (S > V)
2. (T v ~W) > (V > S)
3. T
/S = V
8.
1. (A & B) > C
2. (B > C) > D
3. ~D
/~A
9.
1. (X & Y) > Z
2. X
3. (W & Z) > Y
4. W
/Y = Z
Part 4: Translate the following arguments into symbolic form and use the 18 rules of inference
(the 8 rules of implication and the 10 rules of replacement) to provide logical proofs with line-
by-line justifications. The letters to be used for the simple statements are given in parentheses
after each exercise. Use the letters in the order in which they are used.
10.
Vitamin E is a useless food supplement if and only if it does not reduce heart disease. It is not
the case that either vitamin E does not reduce heart disease or is not an antioxidant. Therefore,
vitamin E is not a useless food supplement and it is an antioxidant (U, R, A)
2
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