If A = {x : x is a positive multiple of 25 less than 100}, how many subsets does A have?
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Answer and explanation
Correct answer: 8
The positive multiples of 25 that are less than 100 are 25, 50, and 75. Thus A has three elements. A set with n elements has 2^n subsets, because each element can either be included or excluded from a subset. Therefore, A has 2^3 = 8 subsets. The strict phrase “less than 100” excludes 100 itself.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The positive multiples of 25 that are less than 100 are 25, 50, and 75. Thus A has three elements. A set with n elements has 2^n subsets, because each element can either be included or excluded from a subset. Therefore, A has 2^3 = 8 subsets. The strict phrase “less than 100” excludes 100 itself.
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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