I need to say whether the system of logical laws made of:
- Double negation
- de Morgans
is sound and whether it is adequate if we remove de Morgan's laws from it, for my mathematical logic paper. I believe I have a derivation showing that $¬(A ∧ B) ⇔ (¬A ∨ ¬B)$ and $¬(A V B) ⇔ (¬A ∧ ¬B)$, without using the law itself, but I need help saying whether this 'system' is sound and adequate.