So, hopefully this is a fitting place to ask.
I have the sentence "If anyone likes Christina, then Didrik does", and the key: Lxy: x likes y d: Didrik c: Christian
I proposed it should be written:
- (∃xLxc) --> (Ldc)
but I friend had chosen to move the brackets, like this:
- ∃x(Lxc --> Ldc)
Unfortunately, we have both only have 1 lecture on Predicate Logic, so our discussion wasn't really that helpful, for none of us were able to really justify our symolization ...
Is anyone here capable explaining if there is any difference, if so, what it is, and perhaps also which is wrong.
Regarding variables: For the sentnece "If someone is attracted to Bjorn, the everyone hates or loves Didrik", with the key: b: Bjorn d: Didrik Axy: x is attracted to y Hxy: x hates y Lxy: x loved y
- ∃xAxb --> ∀x(Hxd v. Lxd)
for I was thinking that if it is the case that at least one person is attracted to Ben, then it is the case the everyone hates or loves Didrik .... (an dhopefully that is what I've written).
At the same time, someone proposed to have different variables for the two qantifiers, like this:
- ∃xAxb --> ∀y(Hyd v. Lyd)
Which one is correct (if any of them are)? Is is correct to say it doesn't matter?