If A = {1, 1, 2, 2, 3} is considered as a set, what is n(P(A))?
Answer and explanation
Correct answer: 8
In set theory, repeated elements do not create new elements. Thus the given collection is the set A = {1,2,3}, whose cardinality is 3 rather than 5. A set with n elements has 2^n subsets, so n(P(A)) = 2^3 = 8. The repeated 1s and 2s must therefore be ignored when determining the number of elements and the size of the power set.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
In set theory, repeated elements do not create new elements. Thus the given collection is the set A = {1,2,3}, whose cardinality is 3 rather than 5. A set with n elements has 2^n subsets, so n(P(A)) = 2^3 = 8. The repeated 1s and 2s must therefore be ignored when determining the number of elements and the size of the power set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
