Halp with Predicate Logic!

[Zephyr]

So I'm doing a predicate logic practice test for my final, but 2 of the questions don't have answers in the back and I need to see if I did them right. Can anybody try and confirm these for me? It's just a matter of taking natural language sentences and symbolizing them in QL.

For reference:

&=and, \/=or, >=If/then, ~=not, {=}= "If and only if", {A}=all, and {E}=Some.

This is because I can't make some of these symbols on computer.

1. "Only fictional characters are immortal." where Fx: "x is a fictional character" and Ix: "x is immortal."

({A}x)(Ix>Fx), ({A}x)(~Fx>~Ix)

. I think these are both right, but I'm not sure if one is better than the other.

2. "Alice both loves and is loved by everyone only if there is at least one blues singer that both loves and is loved by everyone." where Px: x is a person., Bx: x is a blues singer. Lxy: x loves y., and a: Alice.

({A}x)[Px>(Lax&Lxa)]>({E}x)[Bx&({A}y)(Py>[Lxy&Lyx])]

Honestly I'm a lot more worried about the second (for obvious reasons) but either will help muchly.

Gotta love symbolic logic. It can make even relatively simple sentences seem ridiculous and unreadable.

 

[Zephyr]

Also, if anybody knows how to make an upside-down A or backwards E on a computer, that could be helpful for future online communications. Really, any symbolic logic symbols could make things clearer.