I have been trying to solve the following but not sure if I am on the right lines. Please can you help?
1) Logical statement L (c,d) stands for (c knows d) where the discourse universe is a set of people at Ryan's party. Translate the following into logical notations.
(So P stands for party)
a) Ryan knows everyone at the party - ∀xP(x) => L (x)
b) Everyone knows each other - ∀x∀y L(x,y) => L(x,y)
c) There are people who don't know each other - ∀x∃y P(x) => ⌜L(y,x)
d) For any two people who dont know each other, there is someone who knows them both - ∃x ⌜P(x) ^ ∃y L(y,x)
Thanks in advance!