There are many ways to construct these proofs--it'll depend on your logical system and which inference rules you have at your disposal. Feel free to reach out to me if you're still looking for some direction on these!

Sj T.

asked • 10/13/20# Logic: Construct formal proofs for the following

1. A ⊃ (~B ⊃ ~A)

⊢ A ⊃ B

2. ~C

⊢ (D ∧ C) ⊃ E

3. F ⊃ G

F ∨ (H ∧ G)

⊢G

4. ɪ ≡ J

K ∨ ~J

⊢ɪ ⊃ K

## 2 Answers By Expert Tutors

1) A --> (A --> B) by contrapositive

A --> (~A or B) by implication identity

~A or (~A or B) by implication identity

~A or ~A or (~A or B) by distributive

(~A or ~A or ~A) or B by associative

~A or B

A -->B by implication identity

===================================================================

2) Given ~C,

~C = ~C or ~D must hold

= ~(C and D) must hold

This implies ~(C and D) or E must hold

(C and D) -> E

=====================================================

3) If F then F or (H and G)

then F or (H and G) => G

===================================================

4) if K, then ~I or K ---> I-->K

if ~J, then ~I ---> ~I or K ---> I --> K

## Still looking for help? Get the right answer, fast.

Get a free answer to a quick problem.

Most questions answered within 4 hours.

#### OR

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.