Let A be the set of distinct letters in the word MOON. How many elements does P(A) have?
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Answer and explanation
Correct answer: 8
A set records each distinct element only once. Although the word MOON has four positions, the letter O is repeated, so the distinct-letter set is A = {M,O,N}. Thus n(A) = 3. The power set of a three-element set contains 2³ = 8 subsets, including the empty set and A itself. Hence option B is correct.
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 the word MOON has four positions, the letter O is repeated, so the distinct-letter set is A = {M,O,N}. Thus n(A) = 3. The power set of a three-element set contains 2³ = 8 subsets, including the empty set and A itself. Hence option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
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