There are three propositions A, B, C and another condition "some two of these propositions are true and the third one is false", or, in other words, "exactly 2 of 3 propositions are true". Using truth tables and a Karnaugh map (as discussed at How to find the logical formula for a given truth table?) i deducted the Boolean expression for this: ABC' + AB'C + A'BC. Is there any more succinct notation for this expression in any branch of logic?
Edit: Obviously using proposition calculus notation the above statement may be represented as: $(A \wedge B \wedge \neg C) \vee (A \wedge \neg B \wedge C) \vee (\neg A \wedge B \wedge C)$. I am sorry if that misguided you. I'm still interested, if any more succinct notation is possible.