Ivan will be sad if and only if any child is injured.
A) Si ≡ (∃x)(Cx • Ix)
B) (x)[(Cx • Ix) ≡ Ix]
C) (∃x)(Cx • Ix) ⊃ Si
D) Si ≡ (x)(Cx • Ix)
E) Si ≡ (x)(Cx ⊃ Ix)

Question

Quizplus · Accepted Answer

The statement is a biconditional statement (if and only if). This means that both directions of implication are true. Thus, we can break it down into two conditional statements:
1. If any child is injured, Ivan will be sad.
2. If Ivan is sad, then some child must be injured.

A) The existential quantifier (∃x) accounts for the "some child" in statement 2, while the conjunction (Cx • Ix) accounts for the "is injured" part. Therefore, A accurately represents the statement as a whole.

Ivan Will Be Sad If and Only If Any Child