If \(A=\{1,2,3,4\}\) and \(B=\{1,3,5,7\}\), how many ordered pairs \((x,y)\) in \(A\times B\) satisfy \(y=2x-1\)?
Answer and explanation
Correct answer: 4
For every element \(x\) of \(A\), calculate \(y=2x-1\), and then check whether the resulting value belongs to \(B\). The values are \(1,3,5,7\) for \(x=1,2,3,4\), respectively. All four values lie in \(B\), so the valid ordered pairs are \((1,1),(2,3),(3,5),(4,7)\). Therefore, the answer is 4, option C. The condition and membership in both sets must be checked.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
For every element \(x\) of \(A\), calculate \(y=2x-1\), and then check whether the resulting value belongs to \(B\). The values are \(1,3,5,7\) for \(x=1,2,3,4\), respectively. All four values lie in \(B\), so the valid ordered pairs are \((1,1),(2,3),(3,5),(4,7)\). Therefore, the answer is 4, option C. The condition and membership in both sets must be checked.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions.
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