If A = {a, b, c, d}, how many subsets of A do not contain the element a?
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Answer and explanation
Correct answer: 8
A subset that does not contain a must be formed only from the remaining elements {b, c, d}. A three-element set has 2^3 subsets because each element can independently be selected or not selected. Therefore the required number is 2^3 = 8. The number 16 represents all subsets of the original four-element set.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
A subset that does not contain a must be formed only from the remaining elements {b, c, d}. A three-element set has 2^3 subsets because each element can independently be selected or not selected. Therefore the required number is 2^3 = 8. The number 16 represents all subsets of the original four-element set.
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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