If \(A=\{x\mid x\) is a positive multiple of 10 and \(x<50\}\), how many proper subsets does \(A\) have?
Answer and explanation
Correct answer: 15
The positive multiples of 10 that are less than 50 are 10, 20, 30, and 40. Therefore, \(A=\{10,20,30,40\}\) has four elements. A set with \(n\) elements has \(2^n\) subsets in total. Exactly one of these is the set itself, so the number of proper subsets is \(2^4-1=16-1=15\). Thus option B is correct; 16 would count all subsets, including \(A\) itself.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
The positive multiples of 10 that are less than 50 are 10, 20, 30, and 40. Therefore, \(A=\{10,20,30,40\}\) has four elements. A set with \(n\) elements has \(2^n\) subsets in total. Exactly one of these is the set itself, so the number of proper subsets is \(2^4-1=16-1=15\). Thus option B is correct; 16 would count all subsets, including \(A\) itself.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
