If \(A=\{1,3,5,7\}\) and \(B=\{x:x\text{ is a positive odd integer less than }8\}\), what is the relation between A and B?
Answer and explanation
Correct answer: \(A=B\)
The positive odd integers smaller than 8 are 1, 3, 5, and 7. No other positive odd integer satisfies the condition: 9 is not less than 8, while 0 and negative odd integers are not positive. Thus the roster form of B is \(B=\{1,3,5,7\}\), exactly the same as A. Since equal sets contain all and only the same elements, the correct relation is \(A=B\), not a proper-subset relation.
Frequently asked questions
What is the correct answer to this question?
\(A=B\)
Why is this the correct answer?
The positive odd integers smaller than 8 are 1, 3, 5, and 7. No other positive odd integer satisfies the condition: 9 is not less than 8, while 0 and negative odd integers are not positive. Thus the roster form of B is \(B=\{1,3,5,7\}\), exactly the same as A. Since equal sets contain all and only the same elements, the correct relation is \(A=B\), not a proper-subset relation.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
