This question is from the book Abstract Algebra: Theory and Applications by Thomas W. Judson.
Chapter 1 – Question 26
Define a relation $\sim$ on $\mathbb{R}^2$ by stating that $(a, b) \sim (c, d)$ if and only if $a^2 + b^2 \leq c^2 + d^2$. Show that $\sim$ is reflexive and transitive but not symmetric.