Homework SourseProve using a proof sequence that the argument is valid hint
Prove using a proof sequence that the argument is valid (hint: the last A’ has to be inferred). Justify each step with a comment.
(A C) (C B) B A
Solution
Let us prepare tooth table for the given statement
(A C) (C B) B A
| A | B | C | B\' | A-->C | C-->B\' | A-->C ^ C-->B\' | A-->C ^ C-->B\' ^B | A\' |
| T | T | T | F | T | F | F | F | F |
| T | T | F | F | F | T | F | F | F |
| T | F | T | T | T | T | T | F | F |
| T | F | F | T | F | F | F | F | F |
| F | T | T | F | F | F | F | F | T |
| F | T | F | F | T | T | T | F | T |
| F | F | T | T | F | T | F | F | T |
| F | F | F | T | F | F | F | F | T |
