Constructing Truth Tables

# Constructing Truth Tables

## Sheet1

 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