Watson Conditional (If-Then) Reasoning — Questions and Answers
Question 1: A company policy states: 'If an employee is late three or more times in a month, they receive a written warning.' James received a written warning. What can we conclude?
- James was late exactly three times
- James was late at least three times
- James may or may not have been late three times — there could be other reasons for the warning (Correct answer)
- James will be dismissed if he is late again
Correct answer: James may or may not have been late three times — there could be other reasons for the warning
This illustrates affirming the consequent — an invalid inference. The policy says lateness causes a warning (A → B), but it does not say lateness is the ONLY cause of a warning. We cannot reverse the conditional and conclude James was definitely late.
Question 2: 'If the server is overloaded, the website will be slow.' The website is currently running normally. What can we logically conclude?
- The server is not overloaded (Correct answer)
- The server is overloaded but managing the load
- There are very few users on the website right now
- Nothing can be concluded about the server's state
Correct answer: The server is not overloaded
This is modus tollens — a valid deductive form. If 'P → Q' and 'not Q,' then 'not P.' Overload would necessarily cause slowness. Since the website is not slow, the server cannot be overloaded.
Question 3: 'All managers who completed the leadership course received a pay increase. Sandra received a pay increase.' Which reasoning error does concluding 'Sandra must have completed the course' commit?
- Modus ponens — drawing a valid forward inference
- Modus tollens — drawing a valid backward inference
- Affirming the consequent — reversing the conditional invalidly (Correct answer)
- Denying the antecedent — negating both sides invalidly
Correct answer: Affirming the consequent — reversing the conditional invalidly
The original conditional says completing the course is sufficient for a pay increase, not that it is the only cause. Concluding the course was completed from the pay increase alone reverses the direction of the conditional, which is the fallacy of affirming the consequent.
Question 4: 'If a candidate scores above 85% on the aptitude test, they advance to the interview stage.' Tom did not advance to the interview stage. What is a valid conclusion?
- Tom scored exactly 85%
- Tom scored 85% or below (Correct answer)
- Tom did not sit the aptitude test
- Tom scored above 85% but was rejected on other grounds
Correct answer: Tom scored 85% or below
By modus tollens: if 'scoring above 85% → advance' and Tom did not advance, then Tom did not score above 85% — meaning he scored 85% or below. Option D directly contradicts the stated rule. Options A and C are not supported by the information given.
Question 5: A rule states: 'Only certified inspectors may approve a building.' Rafael approved a building. What follows logically?
- Rafael will receive a commendation for his work
- Rafael is a certified inspector (Correct answer)
- Rafael may or may not be a certified inspector
- Rafael bypassed proper procedure
Correct answer: Rafael is a certified inspector
'Only X may do Y' means being X is a necessary condition for doing Y. Unlike 'If X then Y,' this form can be reversed: if Y occurred (approval happened), X must be true (Rafael must be certified). This is one of the few valid reverse inferences.
Question 6: 'If patients take the medication as prescribed, their symptoms will improve.' Maria's symptoms have not improved. What additional information would make it logically certain that Maria did not take the medication as prescribed?
- The medication has no known side effects
- Maria's doctor confirmed the dosage was correct
- The only possible reason symptoms can fail to improve is non-compliance with the prescription (Correct answer)
- Maria's condition worsened before the medication could take effect
Correct answer: The only possible reason symptoms can fail to improve is non-compliance with the prescription
Modus tollens requires that the consequence (improvement) can ONLY fail to appear for one reason. The original conditional doesn't rule out other causes of non-improvement (severity of illness, misdiagnosis, drug interaction). Option C provides the missing premise that makes the modus tollens inference valid.
Watson Conditional (If-Then) Reasoning
A company policy states: 'If an employee is late three or more times in a month, they receive a written warning.' James received a written warning.
What can we conclude?