1. The problem asks to translate the given logical statements into English, assuming the domain for each variable is all real numbers. 2. Statement a) is \(\forall x \exists y (x < y)\). This means "For every real number \(x\), there exists a real number \(y\) such that \(x < y\)." In simpler terms, no matter what number you pick, you can always find a larger number. 3. Statement b) is \(\forall x \forall y (((x \geq 0) \wedge (y \geq 0)) \to (xy \geq 0))\). This means "For all real numbers \(x\) and \(y\), if \(x\) and \(y\) are both greater than or equal to zero, then their product \(xy\) is also greater than or equal to zero." In other words, the product of two nonnegative numbers is nonnegative. 4. Statement c) is \(\forall x \forall y \exists z (xy = z)\). This means "For every real number \(x\) and every real number \(y\), there exists a real number \(z\) such that \(z\) equals the product of \(x\) and \(y\)." Simply put, the product of any two real numbers is also a real number. These translations use the rules of quantifiers: \(\forall\) means "for all" or "every," and \(\exists\) means "there exists." The domain being all real numbers means \(x, y, z\) can be any real number.