Symbolic Logic help

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Homework Statement


Symbolize this statement:
Given that some mean elf will bite and some friendly one will too, the mean ones will bite whether or not provoked but the friendly ones will bite only if provoked.


Homework Equations



let's say A=for all, E=there exists, & is and, (or) is or, ~ is negation, -> is conditional, <-> is biconditional
F(1) is friendly
G(1) is mean
H(1) is an elf
I(1) will bite
J(1) is provoked


The Attempt at a Solution



(Ey ((Hy & Gy) & (Iy → (Jy (or) ~Jy))) & Ey ((Hy & Fy) & (Iy → Jy)))


it wasn't right...
 

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