If \(A\) is the set of distinct letters in the English word MATHEMATICS and \(B\) is the set of distinct letters in the English word STATISTICS, what is \(A\cap B\)?
Answer and explanation
Correct answer: \(\{A,I,M,S,T\}\)
The distinct letters in MATHEMATICS are \(\{M,A,T,H,E,I,C,S\}\), and those in STATISTICS are \(\{S,T,A,I,C\}\). The letters common to both sets are A, I, M, S, and T? On checking, M is not present in STATISTICS, so the correct common set is actually \(\{A,C,I,S,T\}\). Therefore option C is mathematically correct, and the original answer key A must be corrected.
Frequently asked questions
What is the correct answer to this question?
\(\{A,I,M,S,T\}\)
Why is this the correct answer?
The distinct letters in MATHEMATICS are \(\{M,A,T,H,E,I,C,S\}\), and those in STATISTICS are \(\{S,T,A,I,C\}\). The letters common to both sets are A, I, M, S, and T? On checking, M is not present in STATISTICS, so the correct common set is actually \(\{A,C,I,S,T\}\). Therefore option C is mathematically correct, and the original answer key A must be corrected.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
