# Discrete Math: Logic Problems, Truth Table and Rules of Inference

Please see the attached file for the fully formatted problems.

1. Construct the truth table for the compound proposition: [p &#61658;&#61472;(&#61656;q &#61614;&#61472;&#61656;r)] &#61611;&#61472;(&#61656;r &#61614;&#61472;&#61656;p)
p q r
-------------------------------------------------------------
T T T
T T F
T F T
T F F
F T T
F T F
F F T
F F F

2. What is the negation of the quantified statement:
For every integer, x, there is an integer, y, such that x + y = 0.

3. Use the rules of inference to deduce the following conclusion from the following set of premises.
Premises: p &#61658;&#61472;r
r &#61614;&#61472;q
p &#61657;&#61472;s &#61614;&#61472;t
~q
~r &#61614;&#61472;u &#61657;&#61472;s
Conclusion: t

4. Decide if the following is a Valid Argument and justify your reasoning:
All movie stars drive fast cars.
Dan Gordon drives a fast car.
Therefore, Dan Gordon is a movie star.

5. Later in this course, we will study the Inclusion-Exclusion Rule:
|A &#61640;&#61472;B &#61640;&#61472;C| = |A| + |B| + |C| &#61485;&#61472;|A &#61639;&#61472;B| &#61485;&#61472;|A &#61639;&#61472;C| &#61485;&#61472;|B &#61639;&#61472;C| + |A &#61639;&#61472;B &#61639;&#61472;C|.
Verify this for the sets A = {2,3,7,9}, B = {2,3,4}, and C = {1,3,5,7,9}.

6. Find A &#61620;&#61472;B for the sets A = { &#61638;, {&#61638;} } and B = { {&#61638;}, {0} }

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Solution Summary

Logic problems are solved. The solution is detailed and well presented.

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