If A has 7 elements, how many subsets of A must contain one fixed element?
Advertisement
Answer and explanation
Correct answer: 64
Let one particular element be fixed as included. The remaining 6 elements may each be either included or excluded independently. Thus they produce 2^6 possible choices. Every such choice, together with the fixed element, gives one subset containing it. Therefore the required number is 2^6 = 64, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
64
Why is this the correct answer?
Let one particular element be fixed as included. The remaining 6 elements may each be either included or excluded independently. Thus they produce 2^6 possible choices. Every such choice, together with the fixed element, gives one subset containing it. Therefore the required number is 2^6 = 64, so 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.
Advertisement