Consider the set defining the unit circle: 𝐶 = {(𝑥, 𝑦) ∈ ℝ × ℝ: 𝑥 2 + 𝑦 2 = 1}.

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Consider the set defining the unit circle: 𝐶 = {(𝑥, 𝑦) ∈ ℝ × ℝ:
𝑥 2 + 𝑦 2 = 1}. We’ll say 𝑥~𝑦 if and only if (𝑥, 𝑦) ∈ 𝐶. The
relation ~ is over the set ℝ.

Show that ~ is not reflexive.
Show that ~ is symmetric.
Show that ~ is not transitive.
Explain why ~ is not a function from ℝ to ℝ