1. For arbitrary real numbers a & b, exactly one of the three relations hold: a < b, a > b, a = b. How do I state this more formally while also being correct? 2. The attempt at a solution a, b ∈ ℝ ( (a < b) ⊕ ( a > b ) ⊕ ( a = b) ) From this I made a truth table 2^3 entries long, and what we need is for the solution to only be true when exactly one relation is true and the rest false. The xoring works logically for 7 of the 8 entries, but fails when all three values are true. One solution off the top of my head is to simply add the following snippet ( ∧ ¬( (a < b) ∧ ( a > b ) ∧ ( a = b) )). That seems really ugly huh? But is that what the statement (exactly one of the three relations hold) turns into? I am a self learner, anyone want to help me improve? Thank you!