If A = {1, 2, 3} and B = {1, 2, 3, 4, 5}, how many sets X satisfy A ⊆ X ⊆ B?
Answer and explanation
Correct answer: 4
Every set X must contain all elements of A, namely 1, 2, and 3. The only elements that can be chosen freely are 4 and 5, because they belong to B but not to A. Each of these two elements has two independent choices: include it in X or leave it out. Therefore the number of possible sets is 2 × 2 = 2² = 4, including A itself and B itself.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
Every set X must contain all elements of A, namely 1, 2, and 3. The only elements that can be chosen freely are 4 and 5, because they belong to B but not to A. Each of these two elements has two independent choices: include it in X or leave it out. Therefore the number of possible sets is 2 × 2 = 2² = 4, including A itself and B itself.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
