Exercise 1.6 | Q 7.3 | Page 16
Prove that the following pair of statement pattern is equivalent.
p → q and ~ q → ~ p and ~ p ∨ q
1 | 2 | 3 | 4 | 5 | 6 | 7 |
p | q | ~p | ~q | p→q | ~q→~p | ~p∨q |
T | T | F | F | T | T | T |
T | F | F | T | F | F | F |
F | T | T | F | T | T | T |
F | F | T | T | T | T | T |
In the above table, entries in columns 5, 6 and 7 are identical.
∴ Statement p → q and ~q → ~p and ~p ∨ q are equivalent.
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