If A={1,2,3,4}, how many ordered pairs (X,Y) satisfy X⊆Y⊆A and Y=A?
Answer and explanation
Correct answer: 16
The condition Y=A fixes Y completely, so there is only one possible value for the second component. The remaining condition becomes X⊆A, meaning X may be any subset of the four-element set A. A set with four elements has 2^4=16 subsets, including the empty set and A itself. Each choice of X forms exactly one ordered pair (X,A). Therefore, the number of ordered pairs is 16, so option C is correct.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
The condition Y=A fixes Y completely, so there is only one possible value for the second component. The remaining condition becomes X⊆A, meaning X may be any subset of the four-element set A. A set with four elements has 2^4=16 subsets, including the empty set and A itself. Each choice of X forms exactly one ordered pair (X,A). Therefore, the number of ordered pairs is 16, so option C is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
