Formal Proofs with Boolean Connectives
Instructions:
Answer all of the following questions. Type up your answers and submit them to Canvas
for all questions except for the questions you are instructed to submit to the Grade
Grinder which are drawn from the textbook (Language Proof and Logic, 2nd edition);
submit the answers to those questions via the grade grinder. Submit your files to Grade
Grinder in bulk—that is submit them all together. This assignment is due DATE 2021
by 11:59 PM. No late submissions will be accepted.
Total Points: 200
PART I
1. Formal Proofs with Boolean Connectives (Submit your answers to the following
questions to Grade Grinder) (3 points each):
6.3
6.4
6.5
6.6
6.8
6.17
6.18
6.19
6.20
6.24
6.25
6.26
6.27
6.29
6.30
6.33
6.41
6.42
PART II
1. Explain what a necessary condition is and what a sufficient condition is, and then
explain how the material conditional relates necessary and sufficient conditions,
and can be seen to determine the truth values of the material conditional relative to
a set of two atomic sentences. (6 points).
2. Take 6.4, 6.5, 6.6 and 6.8 of the formal proofs from Part I and show that these
instances of logical consequence can be reduced to a logical truth by generating two
truth tables for each proof. The first should demonstrate tautological consequence
and the second should show a tautology. Handwrite the truth tables, take
photographs of them, and insert these photographs into the doc/pdf file you will
submit to Canvas). (4 points each)
3. Explain why if and only if, or biconditional, sentences indicate mutual necessary
and sufficient conditions. Use a joint truth table to help illustrate this. (Produce the
truth table on paper, photograph and embed in your pdf/doc submission to Canvas).
(4 Points).
