Question

write the sentence in symbolic form. represent each component of the sentence with the letter indicated in parentheses. if it is a dog (d), it has fleas (f). options: ~f, d ∧ f, d → f, f → d, d ∨ f

Explanation:

Step1: Recall Conditional Statement

A conditional statement "If \( p \), then \( q \)" is symbolized as \( p
ightarrow q \). Here, \( p \) is "it is a dog (\( d \))" and \( q \) is "it has fleas (\( f \))".

Step2: Match to Symbolic Form

So the symbolic form should be \( d
ightarrow f \) (note: the original option has a typo, likely \( d
ightarrow f \) instead of \( d - f \), but among the options, \( d
ightarrow f \) (interpreted from the option with the arrow) is the correct conditional form for "If \( d \), then \( f \)".

Answer:

\( d
ightarrow f \) (the option labeled as \( d - f \) is likely a typo for \( d
ightarrow f \), so the correct option is the one with \( d
ightarrow f \) (or the option intended to be \( d
ightarrow f \) among the choices, which is the third option if we consider the arrow notation correction).