Select the best translation for this sentence into propositional logic.

Question

A high school principal made this statement to the school board: 

"Either music is not dropped from the curriculum or the students will become cultural philistines; furthermore, the students will not become cultural philistines if and only if music is dropped from the curriculum" [use M, C] 

Select the best translation for this sentence into propositional logic. 

a. ((M v C) · (C ⊃ M))

b.((~M v C) · (~C ⊃ M))

c.((~M v C) · (~C ≡ M))

d.((~M v C) v (~C ≡ M))

Answer 1

c is the answer. Choices a and b do not have if-and-only-if connectives, so they are eliminated. The word "futhermore" translates to AND, so choice d cannot be correct. This leaves c as the only correct choice.