Ambiguity Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
The word 'or' in mathematics is inclusive (pāˆØqp \lor q is true when both hold), but in everyday English 'or' is often exclusive. Show with an example where this causes a mathematical misreading.

Solution

  1. 1
    Everyday: 'You can have cake or pie' usually means one but not both.
  2. 2
    Mathematical: 'A number is even or divisible by 3' is true for n=6n=6 (which is both).
  3. 3
    If a student uses the exclusive interpretation, they might incorrectly exclude n=6n=6 from the solution set.
  4. 4
    Clarification: in mathematics, 'or' is always inclusive unless 'exclusive or' (āŠ•\oplus) is explicitly stated.

Answer

pāˆØqĀ isĀ inclusiveĀ ORĀ ā€”Ā trueĀ evenĀ whenĀ bothĀ pĀ andĀ qĀ holdp \lor q \text{ is inclusive OR ā€” true even when both } p \text{ and } q \text{ hold}
Natural language and mathematical language overlap but differ crucially. Recognising these differences prevents logical errors that arise from importing everyday meanings into formal arguments.

About Ambiguity

A situation where a mathematical expression, statement, or notation can be interpreted in more than one valid way, leading to different results.

Learn more about Ambiguity ā†’

More Ambiguity Examples

Example 1 easy

The expression [formula] is commonly misread. Evaluate it using standard order of operations and exp

Example 3 easy

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Example 4 medium

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