Truth Tables | Homework Help Websites
November 9th, 2018
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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