Solution to Define a binary relation P from R to R as follows: for all real numbers … - Sikademy
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Archangel Macsika

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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For all real numbers x and y,


(x,y)\in P\ \Leftrightarrow x=y^2

P is not a function. For example, (4,2)\in R and also (4,-2)\in R , but 2\neq -2

In other words, an element of the domain is mapped (related) to two different elements of the codomain. So, that's why P is not a function because it doesn't satisfy the property of function.



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