In the Following Proof, Which Justification Is Correct for Line

question 85

Multiple Choice

In the following proof, which justification is correct for line 7? $\begin{array}{llcc} \text {(1) \( (x) \{[\mathrm{C} x \cdot(\mathrm{D} x \vee \mathrm{E} x) ] \supset \mathrm{F} x\} \) } & & \text { Premise} \\ \text { (2) \( (\exists y) (E y * \sim \mathrm{Fy}) \) } & \text {\(/(\exists x) \sim C x\) }& \text { Premise/Conclusion }\\ \text {(3) \( \mathrm{Ea} * \sim \mathrm{Fa} \) } && \text { 2 EI }\\ \text { (4) \( [\mathrm{Ca} \cdot(\mathrm{Da} \cup \mathrm{Ea}) ] D \mathrm{Fa} \) } && \text {\( 1 \mathrm{UI} \) }\\ \text {(5) \( -\mathrm{Fa} \) } && \text {\( 3 \mathrm{Simp} \) }\\ \text { (6) \( \sim[\mathrm{Ca} \cdot(\mathrm{Da} \vee \mathrm{Ea}) ] \) } && \text { \( 4,5 \mathrm{MT} \) }\\ \text { (7) \( \sim \mathrm{Ca} v \sim(\mathrm{Da} v \mathrm{Ea}) ] \) } &\\\end{array}$

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Definitions:

Meso Form

A type of stereoisomer with multiple chiral centers that is superimposable on its mirror image due to a plane of symmetry, rendering it achiral.

Chirality Centers

Specific atoms within a molecule that have four different groups attached, resulting in non-superimposable mirror images.

Chiral Molecule

A molecule that cannot be superimposed on its mirror image, often having a carbon atom bonded to four different groups.

Chiral

Describes a molecule that has a non-superimposable mirror image, often leading to molecules with distinct left-handed (S) and right-handed (R) configurations.