SOLUTION: Use a truth table to determine whether the two statements are equivalent ∼(p → q), p ∧ ∼q

∼(p → q), p ∧ ∼q


| p | q | ~q | p → q | ∼(p → q) | p ∧ ∼q |
———————————————————————————————————————————
| T | T |  F |   T   |     F    |    F    |
| T | F |  T |   F   |     T    |    T    |
| F | T |  F |   T   |     F    |    F    |
| F | F |  T |   T   |     F    |    F    |

The last two columns are the same FTFF, so they
are equivalent and we can now write:

      ∼(p → q) ⇔ p ∧ ∼q

Edwin