Reference no: EM131844807

Assignment: Constructing Truth Tables

In this assignment, you will construct truth tables and use them to assess the validity of arguments.

1. Premise: P → Q

Conclusion: ~P → ~Q

P	Q	P → Q	~P → ~Q
T	T
T	F
F	T
F	F

2. Premise: P → Q

Conclusion: ~Q → ~P

P	Q	P → Q	~Q → ~P
T	T
T	F
F	T
F	F

3. Premise: (P & Q) → R

Q → R

Conclusion: P → R

P	Q	R	P & Q	(P & Q) → R	Q →  R	P →  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

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."

Premise:

Conclusion:

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."

Premise:

Conclusion: