1. The problem statement, all variables and given/known data Suppose P(x) is a statement with a free variable x. Find a formula, using logical symbols, that means "there are exactly two values of x for which P(x) is true." 2. Relevant equations 3. The attempt at a solution (∃x)(∃y)(∀z)(P(x) ∧ P(y) ∧ P(z) → ( x=z ∨ y=z) ∧ x≠y) Is this valid?