Solved

If Anything Is Stuck in Traffic, Bruno Will Be Mad

Question 109

Multiple Choice

If anything is stuck in traffic, Bruno will be mad if it is late. Something is neither annoyed nor not late. If Bruno is mad, then something is annoyed. So something is not stuck in traffic.
-Which of the following is the best translation into M of this argument?


A) (x) [Sx(MbLx) ](x) (AxLx) Mb(x) Ax/(x) Sx\begin{array} { l } ( \forall \mathrm { x } ) [ \mathrm { Sx } \supset ( \mathrm { Mb } \supset \mathrm { Lx } ) ] \\( \forall \mathrm { x } ) \sim ( \mathrm { Ax } \vee \sim \mathrm { Lx } ) \\\mathrm { Mb } \supset ( \exists \mathrm { x } ) \mathrm { Ax } \quad&/(\exists x) \sim S x\end{array}
B) (x) Sx(MbLx) (x) (AxLx) Mb(x) Ax/(x) Sx\begin{array} { l } ( \exists \mathrm { x } ) \mathrm { Sx } \supset ( \mathrm { Mb } \supset \mathrm { Lx } ) \\( \forall \mathrm { x } ) \sim ( \mathrm { Ax } \vee \sim \mathrm { Lx } ) \\\mathrm { Mb } \supset ( \exists \mathrm { x } ) \mathrm { Ax } \quad / ( \exists \mathrm { x } ) \sim \mathrm { Sx }\end{array}
C) (x) Sx(LxMb) (x) (AxLx) Mb(x) Ax(x) Sx\begin{array} { l } ( \exists \mathrm { x } ) \mathrm { Sx } \supset ( \mathrm { Lx } \supset \mathrm { Mb } ) \\( \forall \mathrm { x } ) \sim ( \mathrm { Ax } \vee \sim \mathrm { Lx } ) \\\mathrm { Mb } \supset ( \exists \mathrm { x } ) \mathrm { Ax } \quad \quad ( \exists \mathrm { x } ) \sim \mathrm { Sx }\end{array}
D) (x) [Sx(LxMb) ](x) (AxLx) Mb(x) Ax/(x) Sx\begin{array} { l } ( \forall \mathrm { x } ) [ \mathrm { Sx } \supset ( \mathrm { Lx } \supset \mathrm { Mb } ) ] \\( \forall \mathrm { x } ) \sim ( \mathrm { Ax } \vee \sim \mathrm { Lx } ) \\\mathrm { Mb } \supset ( \exists \mathrm { x } ) \mathrm { Ax } \quad \quad \quad \quad / ( \exists \mathrm { x } ) \sim \mathrm { Sx }\end{array}
E) (x) Sx(LxMb) (x) (AxLx) Mb(x) Ax/(x) Sx\begin{array} { l } ( \forall \mathrm { x } ) \mathrm { Sx } \supset ( \mathrm { Lx } \supset \mathrm { Mb } ) \\( \forall \mathrm { x } ) \sim ( \mathrm { Ax } \vee \sim \mathrm { Lx } ) \\\mathrm { Mb } \supset ( \exists \mathrm { x } ) \mathrm { Ax } \quad / ( \exists \mathrm { x } ) \sim \mathrm { Sx }\end{array}

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