If A = {x : x is a positive perfect-square divisor of 36}, which set is A?
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Answer and explanation
Correct answer: {1, 4, 9, 36}
The positive divisors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. Among these, the perfect squares are 1 = 1², 4 = 2², 9 = 3², and 36 = 6². Therefore A = {1, 4, 9, 36}. Option B omits two valid divisors, option C incorrectly includes 6, and option D contains no perfect-square elements.
Frequently asked questions
What is the correct answer to this question?
{1, 4, 9, 36}
Why is this the correct answer?
The positive divisors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. Among these, the perfect squares are 1 = 1², 4 = 2², 9 = 3², and 36 = 6². Therefore A = {1, 4, 9, 36}. Option B omits two valid divisors, option C incorrectly includes 6, and option D contains no perfect-square elements.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
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