If A = {1, 2, 3}, how many ordered pairs (X, Y) satisfy X ⊆ A, Y ⊆ A, and X ⊆ Y?
Answer and explanation
Correct answer: 27
For each element of A, the condition X ⊆ Y allows exactly three possibilities: the element is in neither X nor Y, it is in Y but not X, or it is in both X and Y. It cannot be in X alone because every element of X must also belong to Y. Since A has three independent elements, the total number of ordered pairs is 3 × 3 × 3 = 3³ = 27.
Frequently asked questions
What is the correct answer to this question?
27
Why is this the correct answer?
For each element of A, the condition X ⊆ Y allows exactly three possibilities: the element is in neither X nor Y, it is in Y but not X, or it is in both X and Y. It cannot be in X alone because every element of X must also belong to Y. Since A has three independent elements, the total number of ordered pairs is 3 × 3 × 3 = 3³ = 27.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
