I'm studying proofs with Vellemans book "How to prove it".
I am having trouble understanding when I am supposed to use the "conjunction" vs "conditional".
My confusion is best illustrated with this example from the book:
Everyone has a roommate who dislikes everyone.
I translated this in the following way:
∀x ∃y ( R(x,y) ∧ ¬∃z L(y,z) )
Where R(x,y) means "x and y are roommates" and L(y,z) means "y likes z".
To me it made intuitive sense to use conjunction. Yet when I looked at the solution in the book, they used the conditional:
∀x ∃y ( R(x,y) → ¬∃z L(y,z) )
I know how their respective truth tables look like and I know that the conditional and the conjunction are not equivalent.
But I lack intuitive understanding of when to use which when translating statements like this one.
