Question

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.

Answer 1

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.