Question: I am studying predicate logic,I came across this para-

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> Propositional logic, studied in Sections 1.1–1.3, cannot adequately express the meaning of all statements in mathematics and in natural language. 
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> For example, suppose that we know that
>  “Every computer connected to the university network is functioning properly.”
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> No rules of propositional logic allow us to conclude the truth of the statement “MATH3 is functioning properly",where MATH3 is one of the computers connected to the university network.
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This is supposed to illustrate the motivation for predicate logic.

*However,we can interpret the given statement as the conjunction of statements of the form "MATHx is connected to the university network and is working properly"*.

As this statement is true and is a conjunction the individual propositions have to be true;in terms of MATH3 too.

*So propositional logic expresses the meaning of the statement adequately and we have also used the rules of propositional logic to conclude the truth about MATH3 contrary to whats been stated*. 

What am I missing?I have gone through the notes by Stephen Simpson and Wikipedia but they proved inadequate.

Answer: 
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> > No rules of propositional logic allow us to conclude the truth of the statement “MATH3 is functioning properly",where MATH3 is one of the computers connected to the university network.
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> This is supposed to illustrate the motivation for predicate logic.
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> *However,we can interpret the given statement as the conjunction of statements of the form "MATHx is connected to the university network and is working properly"*.
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Yes, indeed, and this is the *first step* in moving from propositional logic to predicate logic.

You are no longer discussing a *single* statement about a *single* subject —a proposition—, rather you have moved to discussing a *conjunction* of *similar* statements about *subjects* that belong to a *collection*.

That is on the path to developing quantfied predicate statements.   Next is to move from discussing specific collections, to general collections, and formalise the rules of logic to manage the discussions.
You can express a conjunction such as the following:

"Math1 is connected and working properly AND Math2 is connected and working properly AND ... MathX is connected and working properly",

in propositional logic. However, this does not say that "Every computer connected to the university network is functioning properly." as you have claimed. Why? Because there does not exist any guarantee that the conjunction above covers every computer in the network. You would at least need some clause that says something like "and the only computers on the network are math1, ... mathX".

Unfortunately though, this doesn't answer your question, but it seems too long for a comment, so I'll leave it as a so-called "answer".