in Mathematical Logic edited by
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3 votes
3 votes

Which of the following is a valid inference of $\mathrm{X, Y}$ in first-order logic?
$$
\begin{aligned}
& \text{X}: \forall x .(\mathrm{P}(x) \rightarrow \mathrm{Q}(x)) \\
& \text {Y}: \forall x .(\neg \mathrm{R}(x) \rightarrow \neg \mathrm{Q}(x))
\end{aligned}
$$

  1. $\forall x .(\neg \text{R}(x) \rightarrow \neg \text{P}(x))$
  2. $\forall x .(\mathrm{P}(x) \rightarrow \mathrm{R}(x))$
  3. $\forall x .(\mathrm{R}(x) \rightarrow \mathrm{P}(x))$
  4. $\forall x .(\mathrm{Q}(x) \rightarrow \mathrm{R}(x))$
in Mathematical Logic edited by
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1 Answer

2 votes
2 votes
$\begin{aligned}
& \text{D == Y} \\
& \text{X, Y}\rightarrow \text{B} \\
& \text{B == A}
\end{aligned}$
Answer:

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