Question

match the sentence, strictly speaking, of tfl with its main connective, if there is one, and undefined if there isnt a main connective or it isnt a sentence strictly speaking.$((b \
ightarrow c) \
ightarrow \
eg q)

$$\ eg(d \ ightarrow (p \\vee q))$1. $\ eg$$

(b \vee c \
ightarrow (a \wedge d))$2. $\
ightarrow

$$(\ eg a \ ightarrow b)$3. $\\vee$$

(s \wedge (t \wedge (\
eg r \
ightarrow p)))$4. $\wedge

$$(a \\vee b \\vee c)$5. $\\leftrightarrow$6. undefined$(((\ eg b \\wedge d) \ ightarrow r) \\vee \ eg q)$$

\
eg b \
ightarrow t$

Explanation:

1. For $((B \to C) \to

eg Q)$: The outermost structure is a conditional connecting $(B \to C)$ and $
eg Q$, so main connective is $\to$.

1. For $

eg(D \to (P \vee Q))$: The entire formula is negated, so main connective is $
eg$.

1. For $(B \vee C \to (A \wedge D))$: This is a conditional with $(B \vee C)$ as antecedent, so main connective is $\to$.
2. For $(

eg A \to B)$: This is a standard conditional, main connective is $\to$.

1. For $(S \wedge (T \wedge (

eg R \to P)))$: The outermost connective is conjunction, main connective is $\wedge$.

1. For $(A \vee B \vee C)$: In TFL, disjunction is associative, so main connective is $\vee$.
2. For $(((

eg B \wedge D) \to R) \vee
eg Q)$: The outermost structure is disjunction, main connective is $\vee$.

1. For $

eg B \to T$: This is a conditional with $
eg B$ as antecedent, main connective is $\to$.

Answer:

$((B \to C) \to
eg Q)$ → 2. $\to$
$
eg(D \to (P \vee Q))$ → 1. $
eg$
$(B \vee C \to (A \wedge D))$ → 2. $\to$
$(
eg A \to B)$ → 2. $\to$
$(S \wedge (T \wedge (
eg R \to P)))$ → 4. $\wedge$
$(A \vee B \vee C)$ → 3. $\vee$
$(((
eg B \wedge D) \to R) \vee
eg Q)$ → 3. $\vee$
$
eg B \to T$ → 2. $\to$