Consider the set $C = \{(x,y) : x^2 + y^2 = 1\}$. Then $C$ is a relation of \(\mathbb{

Question

Consider the set $C = \{(x,y) : x^2 + y^2 = 1\}$. Then $C$ is a relation of $\mathbb{R} \times \mathbb{R}$. Consider the set $L = \{(x,y) : y = 2x - 1\}$. Then $L$ is yet another relation of $\mathbb{R} \times \mathbb{R}$. Can you represent these two relations on the Euclidean 2D plane? Representations of $C$ and $L$. For $C$, we can see that $0^2 + 1^2 = 1$ and $0^2 + (-1)^2 = 1$ so that $(0,1), (0,-1) \in C$. Thus, the element $0$ is linked with two distinct elements, namely, $1$ and $-1$. Note also that $2$ is not linked to any element via the relation $C$; i.e., we say that $2$ is not $C$-related to any real numbers. For $L$, every real number $x$ is $L$-related to only one real number $y = 2x - 1$.

Accepted Answer

$C$: unit circle centred at the origin. $L$: line $y=2x-1$. Both representations are shown.

An illustration of two relations on the real line

An illustration of two relations on the real line

Solution:

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