Eduprobe
Question:
The following statement (p→q)→[(¬p→q)→q] is:
a tautology
a fallacy
equivalent to ¬p→q
equivalent to p→¬q
Solution:
| p | q | ¬p | p→q | ¬p→q | (¬p→q)→q | (p→q)→[(¬p→q)→q] |
|---|---|---|---|---|---|---|
| T | T | F | T | T | T | T |
| T | F | F | F | T | F | T |
| F | T | T | T | T | T | T |
| F | F | T | T | F | T | T |
Since all the values in the last column are true, hence the given statement is a tautology.