Ok i found my mistake. im going to post all the truth tables for a- e, if you could just check to make sure i didnt make any errors, that would be awesome! trying to get 100% on this. here they are:

a) i found this proposition was a contradiction. see above ^^ since i made a mistake pointed out once fixed it made it all 1/2 or 1. which i believe is a contradiction.

Code:

T(p) T(q) pVq P^(pVq) p p <-> [p ^ (pVq)]
1 1 1 1 1 1
1 0 1 1 1 1
1 ½ 1 1 1 1
0 1 1 0 0 1
0 0 0 0 0 1
0 ½ ½ 0 0 1
½ 1 1 ½ ½ 1
½ 0 ½ ½ ½ 1
½ ½ ½ ½ ½ 1

p <-> [p ^ (pVq)]

b is a tautology

Code:

T(p) T(q) ~q P ^ ~q P -> q (p -> q) <-> (p ^~q)
1 1 0 0 1 0
1 0 1 1 0 0
1 ½ ½ ½ ½ 1
0 1 0 0 0 1
0 0 1 0 1 0
0 ½ ½ 0 ½ ½
½ 1 0 0 ½ ½
½ 0 1 ½ ½ 1
½ ½ ½ ½ ½ 1

(p -> q) <-> (p ^~q)

c is neither ***check this one*****

Code:

T(p) T(q) ~p ~q ~p ^ ~q pVq ~(pVq) ~(p V q) <-> (~p ^ ~q)
1 1 0 0 0 1 0 1
1 0 0 1 0 1 0 1
1 ½ 0 ½ 0 1 0 1
0 1 1 0 0 1 0 1
0 0 1 1 1 0 1 1
0 ½ 1 ½ ½ ½ ½ 1
½ 1 ½ 0 0 1 0 1
½ 0 ½ 1 ½ ½ ½ 1
½ ½ ½ ½ ½ ½ ½ 1

~(p V q) <-> (~p ^ ~q)

d is a tautology

Code:

T(p) T(q) P ⇔ q ~p q ~p^q ~pVq ~(~pVq) ~(~pVq)V(~p^q) P ⇔ q (p <-> q) <-> ~(~p V q) V (~p^q)
1 1 1 0 1 0 1 0 0 1 0
1 0 0 0 0 0 0 1 1 0 0
1 ½ ½ 0 ½ 0 ½ ½ ½ ½ ½
0 1 0 1 1 1 1 0 1 0 0
0 0 1 1 0 0 1 0 0 1 0
0 ½ ½ 1 ½ ½ 1 0 ½ ½ ½
½ 1 ½ ½ 1 ½ 1 0 ½ ½ ½
½ 0 ½ ½ 0 0 ½ ½ ½ ½ ½
½ ½ ½ ½ ½ ½ ½ ½ ½ ½ ½

(p <-> q) <-> ~(~p V q) V (~p^q)

e is a contradiction ***check this one*****