Homework SourseShow step by step please Thank You Let P be the compound pro
Show step by step please, Thank You.
Let P be the compound proposition ((x rightarrow y) (x doubleheadarrow z)) rightarrow (z y). Using an appropriate truth tree, determine whether or not P is a tautology. If you claim that it is not, give all counterexamples.Solution
Prepare table as follows:
As last two columns are identical it follows that P is a tautology
| x | y | z | ~x | ~y | ~z | x-->~y | x<-->z | (x-->~y)v(x<-->z) | zv~y |
| T | T | T | F | F | F | F | T | T | T |
| T | T | F | F | F | T | F | F | F | F |
| T | F | T | F | T | F | T | T | T | T |
| T | F | F | F | T | T | T | F | T | T |
| F | T | T | T | F | F | T | F | T | T |
| F | T | F | T | F | T | F | T | T | T |
| F | F | T | T | T | F | T | F | T | F |
| F | F | F | T | T | T | F | T | T | T |
