If A = {a, b, c, d, e}, how many subsets of A do not contain a?
Answer and explanation
Correct answer: 16
To form a subset that does not contain a, we may choose elements only from {b, c, d, e}. There are four remaining elements, and each element has two independent choices: it may be included or excluded. Therefore, the number of possible subsets is 2^4 = 16. This includes the empty set and every valid combination of the four allowed elements, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
To form a subset that does not contain a, we may choose elements only from {b, c, d, e}. There are four remaining elements, and each element has two independent choices: it may be included or excluded. Therefore, the number of possible subsets is 2^4 = 16. This includes the empty set and every valid combination of the four allowed elements, 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.
