If U = {1,2,…,100} and A = {x : x is not divisible by 7}, what is |A′|?
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Answer and explanation
Correct answer: 14
A contains the numbers in U that are not divisible by 7. Therefore, its complement A′ contains exactly the multiples of 7 in U. These are 7, 14, 21, …, 98. Their count is floor(100/7) = 14, because 7 × 14 = 98 while 7 × 15 = 105 exceeds 100. Hence |A′| = 14.
Frequently asked questions
What is the correct answer to this question?
14
Why is this the correct answer?
A contains the numbers in U that are not divisible by 7. Therefore, its complement A′ contains exactly the multiples of 7 in U. These are 7, 14, 21, …, 98. Their count is floor(100/7) = 14, because 7 × 14 = 98 while 7 × 15 = 105 exceeds 100. Hence |A′| = 14.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
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