A. Directions. Translate Argument H below using the translation dictionary here:

Question

A.    Directions. Translate Argument H below using the translation dictionary here:

Translation dictionary: E = Eve joins the club, F = the club’s financial position will become more secure, K = Kate will join the club, P = the club’s social prestige rises, T = Toby will join the club.

“~” for all negations. “&” for all conjunctions. “v” for all disjunctions. “->” for all implications; implications are also called conditionals. “<->” for all equivalences; equivalences are also called biconditionals

Argument H: Toby will join the club only if the club’s social prestige rises. Eve’s joining the club is a sufficient condition for the club’s financial position to become more secure. Either Eve or Toby will join. Eve will join if the club’s social prestige rises, and the club’s financial position becoming more secure implies that Kate will join. Hence if Eve doesn’t join, then Kate will.

Explanation / Answer

E = Eve joins the club
F = the club’s financial position will become more secure
K = Kate will join the club
P = the club’s social prestige rises
T = Toby will join the club.

Toby will join the club only if the club’s social prestige rises
P->T

Eve’s joining the club is a sufficient condition for the club’s financial position to become more secure.
E -> F

Either Eve or Toby will join.
E v T

Eve will join if the club’s social prestige rises, and the club’s financial position becoming more secure implies that Kate will join.
(P -> E) & (F -> K)

Hence if Eve doesn’t join, then Kate will.
|- (~E) -> K

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