In the Following Proof, Which Justification Is Correct for Line

question 115

Multiple Choice

In the following proof, which justification is correct for line 11? $\begin{array}{llcc} \text { (1) \( (x) [\mathrm{G} x \supset(y) (\mathrm{H} y \supset \mathrm{I} x y) ] \) } && \text {Premis} \\ \text {(2) \( (\exists x) [\mathrm{G} x \cdot(\exists y) \sim \mathrm{I} x y] \) } &\text { \(I \sim(x) \mathrm{H} x\) }&\text {Premise/Conclusion} \\ \text { (3) \( (x) \mathrm{H} x \) } && \text {Assumption}\\ \text {(4) \( \mathrm{Ga} \cdot(\exists y) \sim \mathrm{Iay} \) } && \text {\( 2 \mathrm{EI} \) }\\ \text {(5) \( \mathrm{Ga} \) } && \text {\( 4 \operatorname{Sinp} \) }\\ \text { (6) ( \( \exists y) \sim \) Iay } && \text {\( 4 \operatorname{Sinp} \) }\\ \text { (7) \( -\mathrm{Iab} \) } & & \text {\( 6 \mathrm{EI} \) } \\ \text {(8) \( \mathrm{Ga} \supset(\mathrm{y}) (\mathrm{Hy} \supset \mathrm{Iay}) \) } && \text {\( 1 \mathrm{UI} \) }\\ \text { (9) \( (\mathrm{y}) (\mathrm{Hy} \supset \mathrm{Iay}) \) } && \text {\( 5,8 \mathrm{MP} \) }\\ \text {(10) \( \mathrm{Hb} \supset \mathrm{Iab} \) } &&\text {\( 9 \mathrm{UI} \) }\\ \text { (11) \( \mathrm{Hb} \) } &\\ &\\\end{array}$

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Definitions:

Mixed-Sex Couple

A romantic or sexual partnership comprising one male and one female individual.

Contraception Method

Various techniques and devices used to prevent pregnancy, including hormonal pills, barriers like condoms, intrauterine devices, and surgical procedures.

Vasectomy

A surgical procedure for male sterilization or permanent contraception.

Tubal Ligation

A surgical procedure used for sterilization in which a woman's fallopian tubes are clamped and blocked, or severed and sealed, to prevent eggs from reaching the uterus for fertilization.