If A has 3 elements, how many ordered pairs (X,Y) are there such that X⊆Y⊆A?
Answer and explanation
Correct answer: 27
Consider each of the 3 elements of A independently. For a pair satisfying X⊆Y⊆A, an element has exactly three possible statuses: it belongs to X (and therefore also to Y), it belongs to Y but not X, or it belongs to neither set. Thus the number of ordered pairs is 3×3×3=3^3=27. The order matters because (X,Y) is an ordered pair, although the containment condition also fixes their relationship.
Frequently asked questions
What is the correct answer to this question?
27
Why is this the correct answer?
Consider each of the 3 elements of A independently. For a pair satisfying X⊆Y⊆A, an element has exactly three possible statuses: it belongs to X (and therefore also to Y), it belongs to Y but not X, or it belongs to neither set. Thus the number of ordered pairs is 3×3×3=3^3=27. The order matters because (X,Y) is an ordered pair, although the containment condition also fixes their relationship.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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