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.
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I won't write natural deduction tree, but make a sketch of the proof.