Practice question · Match the pairs
Match each tool from this unit to the job it does.
- Truth table
- Counterexample
- Induction
- Contradiction
- Refutes a universal claim
- Settles a compound statement in every case
- Proves a claim by ruling out its negation
- Proves a claim for every natural number
Hints
- One tool refutes; three establish.
- Only one of these is tied to the natural numbers specifically.
Show the answer
- Truth table → Settles a compound statement in every case
- Counterexample → Refutes a universal claim
- Induction → Proves a claim for every natural number
- Contradiction → Proves a claim by ruling out its negation
Why
Truth tables settle propositional questions exhaustively; counterexamples refute; induction handles infinitely many discrete cases; contradiction proves indirectly. Together they are the reasoning toolkit this unit has assembled.
Practise The Structure of Mathematical Reasoning
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