Conceptual Dependency Math Example 3

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Example 3

easy
Which concept must be understood before 'proof by contradiction': conditional statements, negation, or both? Explain.

Solution

  1. 1
    Both are required.
  2. 2
    Negation: proof by contradiction begins by assuming the negation of the statement to be proved.
  3. 3
    Conditional: the contradiction found is that a false statement follows, which uses the logic of conditionals and their truth values.

Answer

Both:Ā negationĀ (toĀ negateĀ theĀ goal)Ā andĀ conditionalsĀ (toĀ deriveĀ aĀ contradiction)\text{Both: negation (to negate the goal) and conditionals (to derive a contradiction)}
Conceptual dependencies reveal what must be in place before a new idea can be properly understood. Missing either prerequisite makes the proof technique appear arbitrary or mysterious.

About Conceptual Dependency

The relationship between concepts where understanding one requires prior understanding of another — the prerequisite structure of mathematical knowledge.

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