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.
Show that the following tautology is a theorem of natural deduction
logic;propositional logic