Let A = {x : x is a distinct letter of the English word LEVEL}. How many elements does P(A) have?
Answer and explanation
Correct answer: 8
A set records each distinct element only once. Although LEVEL has five letter positions, the distinct letters are L, E, and V, so A = {L,E,V} and n(A) = 3. The power set of a finite set with n elements contains 2^n subsets. Therefore, n(P(A)) = 2^3 = 8. Repeated occurrences of L and E do not increase the set's cardinality.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
A set records each distinct element only once. Although LEVEL has five letter positions, the distinct letters are L, E, and V, so A = {L,E,V} and n(A) = 3. The power set of a finite set with n elements contains 2^n subsets. Therefore, n(P(A)) = 2^3 = 8. Repeated occurrences of L and E do not increase the set's cardinality.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
