I'm working through some exercises in preparation of a test, I just have the answers, no motivation for why something is wrong. Which is essential in learning imo, so I hope you could give some pointers
C(x, y): x is a child of y.
M(x): x is a man.
W(x): x is a woman.
Write as a predicate:
John or Pete has a child:
My solution: .
The solution given is: .
Is my solution wrong? And so, why? Am I not allowed to use the scope of the quantifier like this in this context? Is my solution solution actually read as 'There's a child that belongs to either John or Pete' by using scope like this?
Everybody has a father and mother:
The given solution:
Again, basically the same question: is my use of scoping correct? Should I prefer to rewrite with the quantifiers out? Is this like not simplifying a fraction?