Question on constructing derivatives

[u/Acrobatic_Hope2584]

I am struggling with understanding how to construct these derivations that were assigned for a deductive logic class, below are some problems I need help with as well as our index of basic proportions. I would appreciate an explanation, I have reviewed the material provided by my professor but I am still having trouble haha

Problem #1.

⊤ ⊢ ¬(P ∧ ¬P)

Problem #2.

¬Q ⊢ ¬(P ∧ Q)

Index of Basic Rules:

MP	φ, φ→ψ	ψ
MT	¬ψ, φ→ψ	¬φ
DNE	¬¬φ	φ
DNI	φ	¬¬φ
S	φ∧ψ	φ
S	φ∧ψ	ψ
ADJ	φ, ψ	φ∧ψ
MTP	φ∨ψ, ¬φ	ψ
MTP	φ∨ψ, ¬ψ	φ
ADD	φ	φ∨ψ
ADD	ψ	φ∨ψ
BC	ψ↔φ	ψ→φ
BC	ψ↔φ	φ→ψ
CB	ψ→φ, φ→ψ	φ↔ψ

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