EDB β€” 00V

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E30

[00V]Let \(X,Y\) sets. Let \(πœ™,πœ“\) logical propositions be; \(x,a\) are free variables in \(πœ™\), and \(y,b\) are free in \(πœ“\). We also assume that \(a,b\) can only be true or false, while \(x∈ X, y∈ Y\). Consider the following formulae. Which ones are well formed? What variables are free in them?

\begin{eqnarray*} b ∧ (βˆ€ x,πœ™) \\ (βˆƒ y, πœ“) ∨ (βˆ€ x,πœ™)\\ βˆ€ x,βˆ€ b, \bigl(πœ™βˆ§ (πœ“βˆ¨ b)\bigr) \\ a ∨ (βˆ€ x,βˆ€ a, πœ™) \\ (βˆƒ x, πœ“) ∧ (βˆ€ x,πœ™) \end{eqnarray*}

Solution 1

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