In the following proof, which justification is correct for line 7? $\begin{array}{llcc}
\text {(1) $ (x)(\sim \mathrm{N} x \supset \mathrm{B} x) $ } && \text {Premise } \
\text { (2) $ (\exists y) \sim \mathrm{By} $ } & \text { $I(\exists z)(\mathrm{N} z \quad \vee \sim \mathrm{C} z)$} & \text { Premise/Conclusion } \
\text { (3) $ \sim \mathrm{Ba} $} &&2 \mathrm{EI} \
\text {(4) $ \sim \mathrm{Na} \supset \mathrm{Ba} $ } && 1 \mathrm{UI} \
\text {(5) $ -\mathrm{Na} 3 $, } &&4 \mathrm{MI} \
\text {(6) $ \mathrm{Na} $ } &&5 \mathrm{DN} \
\text { (7) $ \mathrm{Na} v \sim \mathrm{Cba} $ } &\
\end{array}$

Question

In the following proof, which justification is correct for line 7? $\begin{array}{llcc}
  \text {(1) $ (x)(\sim \mathrm{N} x \supset \mathrm{B} x) $  } && \text {Premise  }  \
 \text { (2) $ (\exists y) \sim \mathrm{By} $ } & \text {  $I(\exists z)(\mathrm{N} z \quad \vee \sim \mathrm{C} z)$} & \text { Premise/Conclusion } \
 \text {  (3) $ \sim \mathrm{Ba} $} &&2 \mathrm{EI} \
 \text {(4) $ \sim \mathrm{Na} \supset \mathrm{Ba} $  } && 1 \mathrm{UI} \
 \text {(5) $ -\mathrm{Na} 3 $,  } &&4 \mathrm{MI} \
 \text {(6) $ \mathrm{Na} $  } &&5 \mathrm{DN} \
\text { (7) $ \mathrm{Na} v \sim \mathrm{Cba} $ } &\
\end{array}$

Quizplus · Accepted Answer

The correct justification for line 7 is "6 Add" because it involves adding a disjunct ($\sim \mathrm{Cba}$) to an existing statement ($\mathrm{Na}$) to form a disjunction ($\mathrm{Na} \vee \sim \mathrm{Cba}$). This is known as the Addition rule in logic.

In the Following Proof, Which Justification Is Correct for Line