1. The problem statement, all variables and given/known data I hope this does not violate copyright or anything but this problem originated from an assignment from Introduction to Mathematical Thinking in Coursera. I could not post there because the class ended and the discussion board there is dead. Let C be the set of all cars, let D(x) mean that x is domestic, and let M(x) meant that x is badly made. Express the following in symbolic form using these symbols: (a) All domestic cars are badly made. (The statement above is fictitious) 2. Relevant equations The professor said that the answer is [strikeout]$$( \exists x \in C)[D(x) \implies M(x)]$$[/strikeout] Corrected: $$( \forall x \in C)[D(x) \implies M(x)]$$ 3. The attempt at a solution My answer Corrected: $$( \forall x \in C)[D(x) = M(x)] $$ [strikeout]$$( \exists x \in C)[D(x) = M(x)] $$[/strikeout] I think it's D(x) = M(x) because all domestic cars are badly made. "Are" is the plural for "is"; therefore, I think an equals (=) sign is neccessary.