# Show that the following tautology is a theorem of natural deduction

I'm struggling to apply the theorems of natural deduction to these two examples.

$$((p \to q) \land (p \to \neg q)) \to \neg p$$

$$((p \to q) \land (p \to r)) \to (p \to (q \land r))$$

Can anyone help? That is, soundness and/or completeness.

• What did you try? Where did you get stuck? We're happy to help with conceptual questions but just answering homework-style exercises for you is unlikely to really help you. – David Richerby Sep 23 '16 at 16:52
• I tried to follow the formula and I think I understand the rules that are necessary to complete the theorem, but I am finding hard to apply them to real case examples. Especially I am having trouble knowing what to assume, reiterate, derive etc. – sebastian Sep 23 '16 at 22:18