# University of California – Berkeley Symbolic Logic Worksheet

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Introduction to Symbolic Logic
Homework 6
Due at 11:59 pm on May 29 (Friday)
Instructions
1. This homework assignment will be challenging in that, unlike the previous ones, no hint
will be provided in the problem statements. But I stick to my syllabus: You are
encouraged to discuss with other students, with your TA, or with me. But you have to
plagiarism. In case you have not known my email discussion style: If you discuss your
homework with me by email, please formulate a specific question or explain the specific
diﬃculty you have, and then I will (i) send to you a hint tailored to your need and (ii) ask
you to give it one more try and then get back to me. Trying to formulate the diﬃculty you
have is an important way of learning.
2. When you construct a derivation in this homework assignment, every step should

either follow one of the 2×4 + 1 basic rules of inference
or cite a derivation that you have constructed in this homework by using just the 2×4
+ 1 basic rules (just like what I did when teaching the “Skip and Revisit” strategy).
3. When you construct a truth table to show that an argument is logically valid, you have to

mark every row in which the premises are all true
and then mark every row in which the conclusion is true.
4. When you construct a truth table to show that an argument is not logically valid, you
have to

mark every row in which the premises are all true but the conclusion is not true.
Problem 6.1
Construct a derivation for each of
the those four arguments:
1.
X⊃Y
————— (10%)
(~Y) ⊃ (~X)
2.
(~X)vY
X
————— (15%)
Y
3.
~(AvB)
————— (25%)
(~A)&(~B)
4.
~(A&B)
————— (25%)
(~A)v(~B)
Problem 6.2 (25%)
The following is my symbolization of a simplified version of Hume’s argument for
inductive skepticism (as mentioned in Unit 1):
G⊃A
A ⊃ (D v I)
~D
(A & I) ⊃ C
C ⊃ (~G)
—————————
~G
Translation Manual (which you won’t really need below)
G: Your justification of induction is good.
A: It is an argument for the thesis that induction is reliable.
D: It is a deductive argument.
I: It is an inductive argument.
C: It is a circular argument.
Decide whether this argument is logically valid, under the following restrictions:

You must state your answer, “Yes” or “No”, to the question of whether it is
logically valid.
You must justify your answer with either method 1 or method 2:
❖ Method 1: Construct a truth table for this argument, and mark the relevant
rows as required on the “instructions” page. (Warning: There will be 25 row
and 5 + 5 + 1 columns and, hence 352 cells in total.)
❖ Method 2: Construct a derivation for this argument. If you make it, you will
show that the answer is “Yes”. If you fail to make it, resort to method 1.

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