Logical reasoning question need help

Question

For each of the following use natural deduction to provide a derivation which shows the argument to be valid.

1. A → B (Use subderivation, not transitivity)

B → C

A → C

2. P → Q

(Q ∨ R) → ~(D ⇔ E)

P → ~(D ⇔ E)

Answer 1

For the first one:

the line on premises 3-5 is to show that they're part of the subproof.

1. A --> B premise |– A --> C
2. B --> C premise
3. | A assume for conditional proof
4. | B 1, 3 modus ponens
5. | C 2, 4 modus ponens
6. A --> C 3-5, conditional proof

and the second goes very similarly:

1. P --> Q premise
2. (Q v R) --> ~(D <--> E) premise
3. | P assumption for conditional proof
4. | Q 1, 3 MP
5. | Q v R 4, disjunction intro
6. | ~(D <--> E) 2, 5 MP
7. P --> ~(D <--> E) 3-6, conditional proof

hope that helps! let me know if you have any questions.