If A = {x, y, z}, how many subsets in P(A) contain x?
Answer and explanation
Correct answer: 4
To form a subset containing x, x must be included, while y and z may each independently be included or excluded. Thus there are 2 choices for y and 2 choices for z, giving 2 × 2 = 4 subsets. They are {x}, {x, y}, {x, z}, and {x, y, z}. The value 8 is the total number of all subsets of A, including those that do not contain x.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
To form a subset containing x, x must be included, while y and z may each independently be included or excluded. Thus there are 2 choices for y and 2 choices for z, giving 2 × 2 = 4 subsets. They are {x}, {x, y}, {x, z}, and {x, y, z}. The value 8 is the total number of all subsets of A, including those that do not contain x.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
