Translating Truth-functional Propositions in QL

1. If Tyler is friendly, then no one is unhappy.
   
   Fx: x is friendly.
   Hx: x is happy
   a: Tyler
   
   Fa  ⊃ ~ (∃x)~Hx
    
2. Someone is studying or someone is partying.
   
   Sx: x is studying
   Px: x is partying
   
   (∃x)Sx v (∃x)Px
    
3. If Bush is re-elected, then there are no Democrats.
   
   Rx: x is reelected
   Dx: x is a Democrat
   a: Bush
   
   Ra ⊃ ~(∃x)Dx
    
4. Something is fishy, but Freda is cool.
   
   Fx: x is fishy
   Cx: x is cool
   a: Freda
   
   (∃x)Fx & Ca
    
5. Everyone runs, just in case something matters.
   
   Rx: x runs
   Mx: x matters
   
   (x)Rx  ≡ (∃x)Mx
    
6. Not everyone is here, but Harry doesn't care.
   
   Hx: x is here
   Cx: x cares
   a: Harry
   
   ~(x)Hx & ~Ca
    
7. If something is hot, and Marty is tired, then something isn't right.
   
   Hx: x is hot
   Tx: x is tired
   Rx: x is right
   a: Marty
   
   ((∃x)Hx & Ta)  ⊃ (∃x)~Rx
    
8. All is well, if Fred is happy.
   
   Wx: x is well
   Hx: x is happy
   a: Fred
   
   Ha ⊃ (x)Wx
    
9. It's not the case that if Tyler isn't bored, then someone is bored.
   
   Bx: x is bored
   a: Tyler
   
   ~(~Ba ⊃ (∃x)Bx)
    
10. Neither everyone is not Icelandic nor is everyone Icelandic.
    
    Ix: x is Icelandic
    ~(x)~Ix & ~(x)Ix