Solution to Define a binary relation P from R to R as follows: for all real numbers … - Sikademy
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Define a binary relation P from R to R as follows: for all real numbers x and y, (x,y)∈P⇔x=y^2. Is P a function? Explain.

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Taking into account that 4=2^2 and 4=(-2)^2, we conclude that (4,2)\in P and (4,-2)\in P. Therefore, the element x=4\in \mathbb R corresponds to two elements y=2\in\mathbb R and y=-2\in\mathbb R, and hence P:\mathbb R\to\mathbb R is not a function y=f(x).


On the other hand, for each element y\in\mathbb R there exists a unique element x=y^2\in\mathbb R. Consequently, P:\mathbb R\to \mathbb R, P(y)=y^2, is a function of variable y.


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