If \(A=\{1,2,3,4\}\) and \(B=\{1,2,3,4\}\), how many ordered pairs \((x,y)\) in \(A\times B\) satisfy \(x+y\leq 5\)?
Answer and explanation
Correct answer: 10
Fix each value of \(x\) and count the allowed values of \(y\). For \(x=1\), all four values of \(y\) work. For \(x=2,3,4\), the numbers of choices are 3, 2, and 1, respectively. Hence the total is \(4+3+2+1=10\). Because ordered pairs are being counted, each distinct position of \(x\) and \(y\) is included, so option C is correct.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
Fix each value of \(x\) and count the allowed values of \(y\). For \(x=1\), all four values of \(y\) work. For \(x=2,3,4\), the numbers of choices are 3, 2, and 1, respectively. Hence the total is \(4+3+2+1=10\). Because ordered pairs are being counted, each distinct position of \(x\) and \(y\) is included, so 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.
