If A has 3 elements, how many ordered pairs (X, Y) are possible such that X ⊆ Y ⊆ A?
Answer and explanation
Correct answer: 27
Consider one particular element of A. Because X ⊆ Y, that element has exactly three permissible statuses: it may belong to neither X nor Y, it may belong to Y but not X, or it may belong to both X and Y. The status “in X but not in Y” is forbidden. Since there are 3 independent elements and 3 choices for each, the total number of ordered pairs is 3 × 3 × 3 = 3³ = 27. Thus option C is correct.
Frequently asked questions
What is the correct answer to this question?
27
Why is this the correct answer?
Consider one particular element of A. Because X ⊆ Y, that element has exactly three permissible statuses: it may belong to neither X nor Y, it may belong to Y but not X, or it may belong to both X and Y. The status “in X but not in Y” is forbidden. Since there are 3 independent elements and 3 choices for each, the total number of ordered pairs is 3 × 3 × 3 = 3³ = 27. Thus option C is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
