You will construct truth tables and use them to assess the

Question

You will construct truth tables and use them to assess the validity of arguments.

1 Premise: P → Q
Conclusion: ~P → ~Q

P	Q

2 Premise: P → Q
Conclusion: ~Q → ~P

P	Q

3 Premise: (P & Q) → R
Q → R
Conclusion: P → R

P	Q	R

4 Translate the following argument and use truth tables to test for validity.

"If 9 is less than 10 and every odd number less than 10 is divisible by 3, then 9 is divisible by 3. THEREFORE If 9 is less than 10 it is less than 10 it is divisible by 3."

N = "9 is less than 10"
O = "Every odd number less than 10 is divisible by 3."
D = "9 is divisible by 3."

N	O	D

5. Translate the following argument and use truth tables to test for validity.

"If it rains tomorrow, I will have a tough commute. If it snows tomorrow, I will have a tough commute. It will either rain or snow tomorrow. THEREFORE I will have a tough commute."

R = "It rains tomorrow."
S = "It snows tomorrow."
T = "I will have a tough commute."

R	S	T