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If \(A=\{1,2,3\}\) and \(B=\{1,2,3,4\}\), how many ordered pairs in \(A\times B\) have the first coordinate greater than the second coordinate?
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Answer and explanation
Correct answer: 3
For each first coordinate \(x\), count the values \(y\in B\) satisfying \(x>y\). If \(x=1\), there are no such values. If \(x=2\), only \(y=1\) works. If \(x=3\), both \(y=1\) and \(y=2\) work. The valid pairs are \((2,1),(3,1),(3,2)\), so the total is \(0+1+2=3\), option B.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
For each first coordinate \(x\), count the values \(y\in B\) satisfying \(x>y\). If \(x=1\), there are no such values. If \(x=2\), only \(y=1\) works. If \(x=3\), both \(y=1\) and \(y=2\) work. The valid pairs are \((2,1),(3,1),(3,2)\), so the total is \(0+1+2=3\), option B.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets.
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