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For example, do you believe that if a shape is a square, then it is a rectangle? But how can that be true if it is not a statement? To be a little more precise, we have two predicates: \(S(x)\) standing for “\(x\) is a square” and \(R(x)\) standing for “\(x\) is a rectangle”. The sentence we are looking at is,

\begin{equation*} S(x) \imp R(x)\text{.} \end{equation*}

This is neither true nor false, as it is not a statement. But come on! We all know that we meant to consider the statement,

\begin{equation*} \forall x (S(x) \imp R(x))\text{,} \end{equation*}

and this is what our convention tells us to consider.

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