If \(A=\{1,2,3\}\) and \(B=\{1,2,3,4,5\}\), how many subsets of \(B\) necessarily contain all elements of \(A\)?
Answer and explanation
Correct answer: 4
A subset of \(B\) that contains \(A\) must include 1, 2, and 3, so those three elements are fixed. Only 4 and 5 remain optional. Each optional element has two independent choices: included or excluded. Therefore, the number of such subsets is \(2^2=4\). They are \{1,2,3\}, \{1,2,3,4\}, \{1,2,3,5\}, and \{1,2,3,4,5\}. Hence option B is correct.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
A subset of \(B\) that contains \(A\) must include 1, 2, and 3, so those three elements are fixed. Only 4 and 5 remain optional. Each optional element has two independent choices: included or excluded. Therefore, the number of such subsets is \(2^2=4\). They are \{1,2,3\}, \{1,2,3,4\}, \{1,2,3,5\}, and \{1,2,3,4,5\}. Hence 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.
