1. Students often have trouble with proofs by contradiction. They don’t understand why when you negate an “if–then” statement, you assume the “if” part and negate the “then” part. Show, using logic tables, that the negation of (p → q) is equivalent to (p∧ ∼ q). Then explain how this equivalence is used as the basis for a proof by contradiction.

2. Give a proof by contradiction that, if 3n + 5 is even, then n must be odd.

**Subject Mathematics Discrete Math**