You just need to learn to use the rules for placing T's and F's
under the columns with ~, ^, v, →, ↔

Rules for putting T or F:

~T becomes F, ~F becomes T
T^T becomes T, anything else with ^ becomes F
FvF becomes F, anything else with v becomes T
T→F becomes F, anything else with → becomes T
T↔T, F↔F both become T, anything else with ↔ becomes F  

Now you fill in the missing T's, F's by the rules above
I've filled the T's and F's under the columns for the
single letters p, q, r.

1.  ~(p^q) 

 p | q | p^q | ~(p^q) |
 T | T |     |        |
 T | F |     |        |
 F | T |     |        |
 F | F |     |        |


2.  ~pv~q    

 p | q | ~p | ~q | ~pV~q) |
 T | T |    |    |        |
 T | F |    |    |        |
 F | T |    |    |        |
 F | F |    |    |        |


3.  (p^q)→(pV~q)  

 p | q | r | ~q | p^q | pV~q | (P^q)→(pV~q) |
 T | T | T |    |     |      |              |
 T | T | F |    |     |      |              |
 T | F | T |    |     |      |              |
 T | F | F |    |     |      |              |
 F | T | T |    |     |      |              |
 F | T | F |    |     |      |              |
 F | F | T |    |     |      |              |
 F | F | F |    |     |      |              |

4. ~q→(p↔r)

 p | q | r | ~q | p↔r | ~q→(p↔r) |
 T | T | T |    |     |          |              
 T | T | F |    |     |          |              
 T | F | T |    |     |          |              
 T | F | F |    |     |          |              
 F | T | T |    |     |          |              
 F | T | F |    |     |          |              
 F | F | T |    |     |          |              
 F | F | F |    |     |          |              

Edwin