Need help to complete it please

Question

I am proving it valid by natural deduction.. Can someone please tell me if there is any mistake

1 B → (C ⇔ D) Premise

2 B Premise

3 ~C Premise

4 C ⇔ D =>E 1,2

5 D → C. =>E 4

6 D. Assumption

7 D → C

8 C =>E 5,7

9 ~C

10 ~D

Answer 1

it looks correct to me!

I'm not sure what all rules of inference you're allowed to use, but another way to do it is on line 6, instead of doing an indirect proof, you could use lines 3 and 5 to get ~D by modus tollens. If you can't use modus tollens, another way to go would be to go from the biconditional on line 4 to (c & d ) v (~c & ~d) by material equivalence. then you can use disjunctive syllogism with that and ~c on line 3 to get (~c & ~d) and then do a conjunction elimination.