If \(A=\{1,2,4,8\}\) and \(B=\{2,4,8,16\}\), how many ordered pairs \((x,y)\) in \(A\times B\) satisfy \(y=2x\)?
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Answer and explanation
Correct answer: 4
For every \(x\in A\), calculate \(y=2x\) and check whether the result belongs to \(B\). The values are \(2,4,8,16\) for \(x=1,2,4,8\), respectively. Therefore, the valid ordered pairs are \((1,2),(2,4),(4,8),(8,16)\). All four satisfy the condition and belong to \(A\times B\), so the answer is 4, option C.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
For every \(x\in A\), calculate \(y=2x\) and check whether the result belongs to \(B\). The values are \(2,4,8,16\) for \(x=1,2,4,8\), respectively. Therefore, the valid ordered pairs are \((1,2),(2,4),(4,8),(8,16)\). All four satisfy the condition and belong to \(A\times B\), so the answer is 4, option C.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
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