<s>[INST] Some sets of people can share information with one another, while other sets of people cannot. Consider the following sets: \(W\) (women), \(X\) (men who are not married to any of \(W\)), and \(Y\) (men married to some of \(W\)). Assume without loss of generality that Alice is in \(W\) and Bob is in \(X\). Explain what information can be shared among the individuals in \(W\), \(X\), and \(Y\).
By information, we mean any message or signal known by one individual that is intended to be communicated to another.
In general, a set of individuals is defined as informationally coherent if information can be shared among all of its members. For example, \(W\) is informationally coherent since information can be shared among all the individuals in \(W\), while \(W\cup X\) is not since no information can be directly shared between any member of \(W\) and any member of \(X\).
Next, let's extend the original groups with new sets \(Z\), \(U\), and \(V\) defined as follows:
\(Z\) (women married to some of \(X\)),
\(U\) (men married to some of \(Z\)),
\(V\) (women married to some of \(Y\)).
Then, which of the new sets \(Z\), \(U\), and \(V\) are informationally coherent with \(W\)?[/INST]