I'm having trouble symbolizing this sentence:
"Every giraffe loves only Alfred."
My thought process was "Every x such that x is a giraffe then it loves something y and y is Alfred."
∀x (Gx → ∃y (L(xy) ∧ y=a))
According to the program I am using, this is incorrect, but I'm not sure where to go from here.
Thanks in advance!
The problem with your approach is that $\exists y(L(xy)\wedge y=a)$ just means that $L(xy)\wedge y=a$ is true for some value of $y$. The only possible value of $y$ that could make it true is $y=a$, so this just says "$x$ loves Alfred" and says nothing about whether $x$ loves anything else. (In other words, $\exists y(L(xy)\wedge y=a)$ is just equivalent to $L(xa)$.)
To express the meaning of "only", you have to break down what "loves only Alfred" really means. If I love only Alfred, that is really two separate statements combined: first, I love Alfred, and second, I don't love anything other than Alfred. Your formula $\exists y(L(xy)\wedge y=a)$ (or $L(xa)$) captures the first statement, but not the second. So, you just have to combine your formula with another one that says $x$ does not love anything other than Alfred.