Identify the contra-positive statement of the conditional statements. If the basketball team score 60 points then the entire students section gets free sweets?

Appeared in: RML Lucknow - 2021

Explanation

The question asks to identify 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 sweets'.
The contrapositive is formed by negating both P and Q and then swapping their order, resulting in the form 'If not Q, then not P'.
Applying this rule, 'not Q' is 'the student section did not get free sweets', and 'not P' is 'the basketball team did not score 60 points'.
Therefore, the contrapositive is 'If the entire student section did not get free sweets, then the basketball team did not score 60 points'.
The contrapositive is logically equivalent to the original conditional statement, meaning if the original statement is true, the contrapositive must also be true.

Option B: This statement is the inverse of the original conditional statement. The inverse has the form 'If not P, then not Q'. It negates both parts but does not reverse their order.
Option C: This statement is the converse of the original conditional statement. The converse has the form 'If Q, then P'. It reverses the order of the parts but does not negate them.
Option D: This statement is a biconditional, indicated by 'if and only if'. It has the form 'P if and only if Q' (P ↔ Q), which means P implies Q and Q implies P. This is a different logical structure and is not equivalent to the original one-way conditional statement.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Logical Equivalence: Contrapositive Statements as background academic context rather than a clinical decision trigger.
While not a clinical question, logical reasoning is a cornerstone of safe and effective nursing practice.
Nurses use 'if-then' logic constantly for clinical decision-making. For example, 'If a patient's blood sugar is below 70 mg/dL, then I will administer glucose.' The contrapositive is also true: 'If I did not administer glucose, then the patient's blood sugar was not below 70 mg/dL.'.
Understanding these logical relationships helps in interpreting protocols, troubleshooting care plans, and ensuring that actions are based on sound reasoning.

How to Approach the Question

First, identify that the question is asking for a specific logical transformation: the contrapositive.
Break down the original conditional statement ('If P, then Q') into its two components: the hypothesis (P) and the conclusion (Q).
P = 'The basketball team scores 60 points.'
Q = 'The entire student section gets free sweets.'
Recall the rule for forming a contrapositive: Negate both components and reverse their order to get 'If not Q, then not P'.
Formulate the 'not Q' and 'not P' statements: 'not Q' is 'the student section did not get free sweets', and 'not P' is 'the basketball team did not score 60 points'.

Concept Tested & Keywords

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Practise the full RML Lucknow - 2021

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