Symbolic Logic Homework: Mean & Friendly Elves Bite

[hjqusai]

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...

 

[mighty2000]

I'm sorry, but your attempt at a solution is not completely correct. Here is a possible correct symbolization for the given statement:

A: All elves are either mean or friendly.
E: There exists an elf who will bite.
F: There exists a friendly elf.
G: There exists a mean elf.
H: For all elves, if they are mean, they will bite whether or not provoked.
I: For all elves, if they are friendly, they will bite only if provoked.

Symbolization:

(A -> (E & (F (or) G))) & ((H & I) -> (J (or) ~J))

Explanation:

The first part of the statement, "Given that some mean elf will bite and some friendly one will too," can be symbolized as "A -> (E & (F (or) G))," which means that if all elves are either mean or friendly, then there exists at least one elf who will bite.

The second part of the statement, "the mean ones will bite whether or not provoked but the friendly ones will bite only if provoked," can be symbolized as "(H & I) -> (J (or) ~J)," which means that if an elf is mean and provoked, or if an elf is friendly and provoked, then they will bite. However, if an elf is friendly and not provoked, they will not bite.

Therefore, the final symbolization is:

(A -> (E & (F (or) G))) & ((H & I) -> (J (or) ~J))