1. The problem asks to translate the logical statement \(\forall x \exists y (x < y)\) into English, where the domain for each variable is all real numbers. 2. The symbol \(\forall x\) means "for all real numbers \(x\)". 3. The symbol \(\exists y\) means "there exists a real number \(y\)". 4. The inequality \(x < y\) means "\(x\) is less than \(y\)". 5. Putting it all together, the statement says: "For every real number \(x\), there exists a real number \(y\) such that \(x\) is less than \(y\)." 6. In simpler terms, this means: "No matter what real number you pick, you can always find a bigger real number."