If \(A=\{1,2,3\}\) and \(B=\{2,4,6,8\}\), how many ordered pairs \((x,y)\) in \(A\times B\) have \(y/x\) as an integer?
Answer and explanation
Correct answer: 9
For each possible first component \(x\), test all elements of \(B\). When \(x=1\), the quotients \(2,4,6,8\) are all integers, giving four pairs. When \(x=2\), the quotients \(1,2,3,4\) are also all integers, giving four more pairs. When \(x=3\), only \(y=6\) works because \(6/3=2\); the other values do not give integers. Thus the total is \(4+4+1=9\), so option C is correct.
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
For each possible first component \(x\), test all elements of \(B\). When \(x=1\), the quotients \(2,4,6,8\) are all integers, giving four pairs. When \(x=2\), the quotients \(1,2,3,4\) are also all integers, giving four more pairs. When \(x=3\), only \(y=6\) works because \(6/3=2\); the other values do not give integers. Thus the total is \(4+4+1=9\), so option C is correct.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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