Key

1. Use symbols (p, q, r) as needed to write the logical form of the argument. Either use truth tables to determine the validity of the argument or identify the rule of inference/error that guarantees its validity/falsity.

Argument	Symbolic Representation
If at least one of these two numbers is divisible by 6, then the product of these two numbers is divisible by 6. The product of these two numbers is not divisible by 6. \ Neither of these two numbers is divisible by 6.

2. Design a circuit for this input/output table. Use either Theorem 1.1.1 or a Karnaugh map to reduce this circuit. Then draw your reduced circuit.

p	q	r	S
0	0	0	1
0	0	1	0
0	1	0	1
0	1	1	1
1	0	0	0
1	0	1	0
1	1	0	0
1	1	1	0

3. Use Theorem 1.1.1 to show that ~(p Ú q) Ú ~p º ~p. (Show your work, you do not have to provide the name for each law you utilize, but write it down if you know it.)