Consider the world in which there are only four propositions, A, B, C and D. How...
Consider the world in which there are only four propositions, A, B, C and D. How many models are there for the following sentences? You must explain what a model is, and justify your answer.
a.) A & B & C & D
b.) A V B V C
c.) A & C
Homework Answers
1) A&B&C&D
| A | B | C | D | A&B&C&D |
| F | F | F | F | F |
| F | F | F | T | F |
| F | F | T | F | F |
| F | F | T | T | F |
| F | T | F | F | F |
| F | T | F | T | F |
| F | T | T | F | F |
| F | T | T | T | F |
| T | F | F | F | F |
| T | F | F | T | F |
| T | F | T | F | F |
| T | F | T | T | F |
| T | T | F | F | F |
| T | T | F | T | F |
| T | T | T | F | F |
| T | T | T | T | T |
There is just one model for which the sentence is true.
2) A V B V C
| A | B | C | A V B V C |
| F | F | F | F |
| F | F | T | T |
| F | T | F | T |
| F | T | T | T |
| T | F | F | T |
| T | F | T | T |
| T | T | F | T |
| T | T | T | T |
There will be seven model for which the sentence will be true.
c) A&C
| A | C | A &C |
| F | F | F |
| F | T | F |
| T | F | F |
| T | T | T |
There will be just one model for which the sentence will be true.
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