# Exercise 7.67#

Suppose \(π \) is a person alive throughout the interval \(π\). Apply the above definition to the example \(π(π ,π‘)\) = βperson \(π \) is worried about news \(π‘\)β from Example 7.65. Here, \(π(π)\) is the set of items that are in the news throughout the interval \(π\).

What open subset of \(π\) is \(β(π‘: π). π(π ,π‘)\) for a person \(π \)?

Does it have the semantic meaning youβd expect, given the less formal description in Section 7.4.4?

## Alternative answer#

It returns the largest open set \(V β U\) for which \(p(s|_V,t) = V\) holds for all \(t β T(V)\). That is, it returns the largest open set where restricting the person \(s\) to the interval \(V\) is still the whole interval \(V\) for all active news items. As in Example 7.65, this corresponds to when the person is worried about *everything* in the news (rather than just *something* i.e. *at least one thing*).