Set A is the set of all positive multiples of 10 that are less than 100. How many elements does it contain?
Answer and explanation
Correct answer: 9
The governing concept is the cardinality of a finite set. The positive multiples of 10 below 100 are obtained as 10n with n = 1, 2, ..., 9: 10, 20, 30, 40, 50, 60, 70, 80, and 90. Since “less than 100” excludes 100, there are 9 distinct elements. Therefore option B is correct; 8 omits one multiple, 10 includes 100, and the set is not infinite.
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
The governing concept is the cardinality of a finite set. The positive multiples of 10 below 100 are obtained as 10n with n = 1, 2, ..., 9: 10, 20, 30, 40, 50, 60, 70, 80, and 90. Since “less than 100” excludes 100, there are 9 distinct elements. Therefore option B is correct; 8 omits one multiple, 10 includes 100, and the set is not infinite.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
