If \(A=\{x:x\text{ is a letter of the English word “math”}\}\) and \(B=\{m,a,t,h\}\), which statement is correct?
Answer and explanation
Correct answer: \(A=B\)
The distinct letters occurring in the word “math” are m, a, t, and h. Therefore the verbal description of set A gives exactly \(A=\{m,a,t,h\}\), which is the same as set B. In set theory, the order in which elements are written does not matter, and repeated elements would also be written only once. Hence A and B have precisely the same elements, so \(A=B\). A proper-subset statement would be false because neither set has an extra element.
Frequently asked questions
What is the correct answer to this question?
\(A=B\)
Why is this the correct answer?
The distinct letters occurring in the word “math” are m, a, t, and h. Therefore the verbal description of set A gives exactly \(A=\{m,a,t,h\}\), which is the same as set B. In set theory, the order in which elements are written does not matter, and repeated elements would also be written only once. Hence A and B have precisely the same elements, so \(A=B\). A proper-subset statement would be false because neither set has an extra element.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
