Identify the contrapositive of the conditional statement: 'If the basketball team scores 60 points, then the entire student section gets free tickets.'

Appeared in: RML 2023

Explanation

The question asks for the contrapositive of a given conditional statement.
A conditional statement has the form 'If p, then q'. In this case, p is 'the basketball team scores 60 points' and q is 'the entire student section gets free tickets'.
The contrapositive is formed by negating both parts and swapping their order, resulting in the form 'If not q, then not p'.
Applying this rule, 'not q' is 'the entire student section did not get free tickets', and 'not p' is 'the basketball team did not score 60 points'.
Combining these gives the correct contrapositive: 'If the entire student section did not get free tickets, then the basketball team did not score 60 points.'.

Option B: This statement negates both the hypothesis and the conclusion but does not swap their order. This form ('If not p, then not q') is known as the inverse.
Option C: This statement swaps the hypothesis and the conclusion but does not negate them. This form ('If q, then p') is known as the converse.
Option D: This statement creates a biconditional relationship ('p if and only if q'), which is a much stronger claim than the original conditional statement. It implies that the two events must always occur together.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Logical reasoning: Identifying the contrapositive of a conditional statement as background academic context rather than a clinical decision trigger.
While not a clinical question, logical reasoning is a fundamental skill for nurses. It is used to interpret patient data, understand cause-and-effect in pathophysiology, and make sound clinical judgments.
For example, a nurse might reason: 'If a patient has symptom X (p), then they might have condition Y (q).' The contrapositive is also true: 'If the patient does not have condition Y (q), they will not have symptom X (p).' This helps in differential diagnosis.
What if? - If the question had asked for the 'inverse', the correct answer would be 'If the basketball team does not score 60 points, then the entire student section will not get free tickets.' This highlights the importance of knowing the precise logical term.

How to Approach the Question

First, identify the structure of the original statement as a conditional 'If p, then q' statement.
Clearly define the 'p' part (the hypothesis) and the 'q' part (the conclusion).
Recall the specific rule for forming a contrapositive: negate both p and q, and then swap their positions to get 'If not q, then not p'.
Formulate the 'not q' and 'not p' statements by negating the original parts.
Construct the final contrapositive statement by combining 'If not q' and 'then not p'.
Carefully compare this constructed statement with each of the given options to find the exact match.

Concept Tested & Keywords

Concept Tested: Logical reasoning: Identifying the contrapositive of a conditional statement.
Stem keywords: conditional statement, contrapositive, basketball team, scores 60 points, student section, free tickets
Lead-in keywords: Identify

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E6 Psychology Morgan King 9e Part 2 p. 67-69

Practise the full RML 2023

Attempt every question from this paper in a timed mock, then review the full solution for each one.