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.

Function is a some rule according to which for every value from domain exists exactly one value from the range that matches to it in terms of the rule

In the given case x is a domain, y is a range, $x=y^{2}$ is a rule. We can tell that if x = 4, than y can be 2 or (-2). So, the condition of the function isn't met.

P is not a function