If \(A=\{0,2,4\}\) and \(B=\{1,3,5\}\), how many ordered pairs in \(A\times B\) have the second coordinate exactly 1 greater than the first coordinate?
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Answer and explanation
Correct answer: 3
The condition says that the second coordinate is one more than the first, so \(y=x+1\). Substituting each element of \(A\) gives \(1,3,5\) for \(x=0,2,4\), respectively. Every resulting value belongs to \(B\), producing the pairs \((0,1),(2,3),(4,5)\). Thus there are exactly 3 pairs, and option C is correct.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
The condition says that the second coordinate is one more than the first, so \(y=x+1\). Substituting each element of \(A\) gives \(1,3,5\) for \(x=0,2,4\), respectively. Every resulting value belongs to \(B\), producing the pairs \((0,1),(2,3),(4,5)\). Thus there are exactly 3 pairs, and option C is correct.
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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