If A = {1, 2, 3, 4}, how many subsets B ⊆ A satisfy that A \ B has exactly 2 elements?
Answer and explanation
Correct answer: 6
For A \ B to contain exactly 2 elements, we must choose exactly 2 elements of A to be excluded from B. Once those two elements are chosen, the other two elements must belong to B, so each choice determines exactly one valid subset B. The number of choices is the combination 4 choose 2, equal to 4!/(2!2!) = 6. Hence six subsets satisfy the condition.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
For A \ B to contain exactly 2 elements, we must choose exactly 2 elements of A to be excluded from B. Once those two elements are chosen, the other two elements must belong to B, so each choice determines exactly one valid subset B. The number of choices is the combination 4 choose 2, equal to 4!/(2!2!) = 6. Hence six subsets satisfy the condition.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
