Working on the book: Daniel J. Velleman. "HOW TO PROVE IT: A Structured Approach, Second Edition" (p. 80)
Example 2.2.2
2. Everyone likes at least two people.
The symbolisation given in the book is:
$$
\forall x \exists y\exists z(L(x,y) \land L(x,z) \land y \neq z)
$$
My symbolisation is:
$$
\forall x \exists y\exists z(L(x,y) \land L(x,z) \land x \neq y \land y \neq z \land x \neq z)
$$
In that same page, the author specifies that the statement means that everyone likes at least two different people. The symbolisation given by the author does not out rule the possibility that a person loves himself/herself, I think, so I added $x \neq y$ and $y \neq z$.
Is my interpretation correct?
Best Answer
Certainly, but that is not a restriction that is indicated by the statement "Everyone likes at least two people". So why would you think that you need to add it?
Just translate what is literally said.