If A = {1, 1, 2, 2, 3}, what is the number of actual elements in A?
Answer and explanation
Correct answer: 3
The defining property of a set is that repetition does not create additional elements. In A = {1, 1, 2, 2, 3}, the repeated entries are written more than once, but each value is counted only once. Therefore the set is equivalent to A = {1, 2, 3}, whose cardinality is 3. Option C is correct; 5 and 4 count repetitions, while 2 omits one distinct value.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
The defining property of a set is that repetition does not create additional elements. In A = {1, 1, 2, 2, 3}, the repeated entries are written more than once, but each value is counted only once. Therefore the set is equivalent to A = {1, 2, 3}, whose cardinality is 3. Option C is correct; 5 and 4 count repetitions, while 2 omits one distinct value.
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.
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