If \(A=\{1,2,3\}\) and \(B=\{1,2,3,4,5\}\), how many ordered pairs \((x,y)\) in \(A\times B\) satisfy \(y-x\ge2\)?
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Answer and explanation
Correct answer: 6
Count the allowable values of \(y\) for each value of \(x\). If \(x=1\), then \(y\ge3\), so \(y=3,4,5\): three pairs. If \(x=2\), then \(y\ge4\), so \(y=4,5\): two pairs. If \(x=3\), then \(y\ge5\), so only \(y=5\): one pair. Hence the total is \(3+2+1=6\), making option A correct.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
Count the allowable values of \(y\) for each value of \(x\). If \(x=1\), then \(y\ge3\), so \(y=3,4,5\): three pairs. If \(x=2\), then \(y\ge4\), so \(y=4,5\): two pairs. If \(x=3\), then \(y\ge5\), so only \(y=5\): one pair. Hence the total is \(3+2+1=6\), making option A correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
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