Exam-style question
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A programmer writes the following Python function to return True when exactly two of three switches are on.\n\ndef exactly_two(a, b, c):\n return (a and b) or c\n\na) Explain why this solution is incorrect.\nb) Give a corrected Boolean expression for the return statement.\nc) Describe a systematic way to check that the corrected solution works.
Model answer
What a good answer should say
- a) The expression returns True whenever c is True, even if neither a nor b is True or if all three switches are True.
- It therefore does not require exactly two true inputs.
- b) A corrected expression is (a and b and not c) or (a and c and not b) or (b and c and not a).
- c) List and test all eight possible combinations of three Boolean inputs.
Explanation
Why this works
For exactly two true inputs, the solution must identify each possible pair and explicitly require that the remaining input is false. Three Boolean inputs have 2^3 = 8 combinations, so checking all eight combinations provides a complete check for this problem.
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