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Truth Tables | Homework Help Websites

Sheet 1

M5.A1 Truth Table Exercises
Back-up QUESTION SET
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:
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.”
Premise:
Conclusion ANSWER:
R S T

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