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What this chapter covers:
Type A: Proving "if p, then q" using Contrapositive
Type B: Proving Irrationality using Contradiction
Problem:
Given:
Answer:
❌ Mistake 1: Incorrectly negating a statement when using proof by contradiction or contrapositive.
❌ Mistake 2: Failing to show a genuine contradiction in proof by contradiction.
When using proof by cases, make sure that all possible cases are covered and that the cases are mutually exclusive to avoid overlap.
What this chapter covers:
Type A: Proving Summation Formulas using Mathematical Induction
Type B: Proving Set Inclusion
Problem:
Given:
Answer:
❌ Mistake 1: Forgetting to prove the base case in mathematical induction.
❌ Mistake 2: Incorrectly applying the inductive hypothesis.
When proving set theory statements, use Venn diagrams to visualize the relationships between sets and guide your proof.