English sentence into TFL

Question

F: Bert will vacation in France.

G: Bert will vacation in Germany.

H: Ernie will vacation in France.

I: Ernie will vacation in Germany.

J: Bert will get a job promotion.

K: Ernie will get a job promotion.

1) Neither Bert nor Ernie will vacation in Germany.

2) Exactly one of the two will vacation in France.

3) Bert will get a job promotion if Ernie doesn't, and vice versa, although both of them will be vacationing in Germany.

Answer 1

Given the provided letters, the statements would be symbolized as follows in most contemporary symbolic logic systems:

∧ represents and/conjunction

∨ represents common inclusive disjunction "or"

~ represents not/negation

1) ~G ∧ ~I

2) Most symbolic logic systems do not have an exclusive or operator, or we would just represent this as F xor H. The common inclusive or operator allows for both terms to be true, so under most systems we have to combine it with a clarifying conjunction: (F ∨ H) ∧ ~(F ∧ H)

3) (~K → J) ∧ (~J → K) ∧ G ∧ I