# 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 (q r)] (r 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 r

r q

p s t

~q

~r u 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 B C| = |A| + |B| + |C| |A B| |A C| |B C| + |A B 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 B for the sets A = { , {} } and B = { {}, {0} }

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#### Solution Summary

Logic problems are solved for discrete mathematics. The truth tables and rule of inferences are analyzed. The solution is detailed and well presented.