Explanation
Given Information
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Total students: n(U)=40
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Students who drink Sprite: n(S)=22
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Students who drink Sprite but not Pepsi: n(S−P)=10
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Claim in Assertion A: The number of students who drink both Sprite and Pepsi, n(S∩P), is 15.
Concept
For any two finite sets A and B, the set A can be divided into two disjoint parts:
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Elements only in A (denoted as A−B).
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Elements common to both A and B (denoted as A∩B).
The fundamental formula is:
Explanation
1. Evaluating Reason (R):
The statement n(A)=n(A−B)+n(A∩B) is a standard identity in set theory. Since (A−B) and (A∩B) are mutually exclusive and their union is A, the equation is mathematically correct.
2. Evaluating Assertion (A):
Using the formula from Reason (R) and applying it to the given data:
Substitute the given values:
The calculated value is 12, but the Assertion claims it is 15.
Final Answer
Based on the analysis:
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Assertion (A) is False.
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Reason (R) is True.
