If A = {1, 2, 3, 4, 5, 6}, how many subsets do not contain 2?
Answer and explanation
Correct answer: 32
To form a subset that does not contain 2, we must exclude 2 and may choose freely from the remaining five elements: 1, 3, 4, 5, and 6. Each of these five elements has two choices, included or excluded. Hence the number of valid subsets is 2⁵ = 32. The total number 2⁶ = 64 includes subsets both with and without 2, while 48 is not a power of two and 16 corresponds to only four freely chosen elements.
Frequently asked questions
What is the correct answer to this question?
32
Why is this the correct answer?
To form a subset that does not contain 2, we must exclude 2 and may choose freely from the remaining five elements: 1, 3, 4, 5, and 6. Each of these five elements has two choices, included or excluded. Hence the number of valid subsets is 2⁵ = 32. The total number 2⁶ = 64 includes subsets both with and without 2, while 48 is not a power of two and 16 corresponds to only four freely chosen elements.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
