~(𝑝→𝑞) ≡ 𝑝∧∼𝑞

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

This is true in all 4 cases, so it's called a tautology".

Rules  (You should learn them).
 
~  means to change what follows ~ to F if it's T, and to T if it's F.

→  means to put T in all cases except when there's a T on the left of → and an F on the right of →.

≡  means to put a T if the same letter (T or F) is on both sides of ≡.

∧  means to put an F unless there are T's on both sides, then you put T.

v  means to put a T unless there are F's on both sides, then you put F (There were none of these v in this problem.)

Edwin