- #1

mr_persistance

- 7

- 2

**1. For arbitrary real numbers a & b, exactly one of the three relations hold:**

a < b, a > b, a = b.

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!