1. The problem statement, all variables and given/known data Let: P(x) = "x is a clear explanation" Q(x) = "x is satisfactory" R(x) = "x is an excuse" x be the domain of all English texts Translate: 1. Some excuses are unsatisfactory 2. All clear explanations are satisfactory 2. Relevant equations ∃ for "some" 3. The attempt at a solution (1) ∃x(R(x) → ~Q(x)) I don't understand why this is not the correct translation. The answer is ∃x(R(x) ∨ ~Q(x)), and I understand that the truth tables for these two are not equivalent, but when I read my answer, it makes sense: "There exists an x such that if x is an excuse, then x is unsatisfactory."I tried reasoning that there is no "If..then" which is why AND was used instead, but for problem (2), the answer is ∀x(P(x)→Q(x)) even when the statement doesn't contain at "If...then".