If \(A=\{-2,-1,0,1,2\}\) and \(B=\{-1,0,1\}\), how many ordered pairs \((x,y)\) in \(A\times B\) satisfy \(x+y=0\)?
Answer and explanation
Correct answer: 3
The equation \(x+y=0\) is equivalent to \(y=-x\). We must ensure that the first component belongs to A and the second belongs to B. For \(x=-1\), \(y=1\); for \(x=0\), \(y=0\); and for \(x=1\), \(y=-1\). These give \((-1,1),(0,0),(1,-1)\). Values \(x=-2\) and \(x=2\) would require 2 and -2, neither of which is in B. Therefore, the answer is 3, option B.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
The equation \(x+y=0\) is equivalent to \(y=-x\). We must ensure that the first component belongs to A and the second belongs to B. For \(x=-1\), \(y=1\); for \(x=0\), \(y=0\); and for \(x=1\), \(y=-1\). These give \((-1,1),(0,0),(1,-1)\). Values \(x=-2\) and \(x=2\) would require 2 and -2, neither of which is in B. Therefore, the answer is 3, option B.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
