true are both engineers(subset(managers engineersmanagers true all people is superset of managers managers engineers {'tom''vic''ann''bob'who is in one but not both(managers engineers(managers engineers{'sue'intersectionyou can find more details on set operations in the python library manual and some mathematical and relational database theory texts also stay tuned for ' revival of some of the set operations we've seen herein the context of dictionary view objects in python booleans some may argue that the python boolean typeboolis numeric in nature because its two valuestrue and falseare just customized versions of the integers and that print themselves differently although that' all most programmers need to knowlet' explore this type in bit more detail more formallypython today has an explicit boolean data type called boolwith the values true and false available as preassigned built-in names internallythe names true and false are instances of boolwhich is in turn just subclass (in the objectoriented senseof the built-in integer type int true and false behave exactly like the integers and except that they have customized printing logic--they print themselves as the words true and falseinstead of the digits and bool accomplishes this by redefining str and repr string formats for its two objects because of this customizationthe output of boolean expressions typed at the interactive prompt prints as the words true and false instead of the older and less obvious and in additionbooleans make truth values more explicit in your code for instancean infinite loop can now be coded as while trueinstead of the less intuitive while similarlyflags can be initialized more clearly with flag false we'll discuss these statements further in part iii againthoughfor most practical purposesyou can treat true and false as though they are predefined variables set to integers and most programmers had been preassigning true and false to and anywaythe bool type simply makes this standard its implementation can lead to curious resultsthough because true is just the integer with custom display formattrue yields integer in pythontype(trueisinstance(trueinttrue other numeric types