If you have Class A with an instance var "foo" which has a @property/@synthesize directive, and Class B inherits from Class A, does it also need to @property/@synthesize "foo"? The reason I ask is because when I try to use Class B's "foo", the calling class says that "foo" is not something of a structured union or a member, which makes me believe it needs to be explicitly synthesized.
No, you don't. Synthesized properties are added to class A and it's subclasses automatically.
WHen inheriting you should not need to redeclare any properties or variables.
Perhaps if you post your ClassB header file or a portion of then people can better pinpoint your problem.
If you have Class A with an instance var "foo" which has a @property/@synthesize directive, and Class B inherits from Class A, does it also need to @property/@synthesize "foo"?
No.
The reason I ask is because when I try to use Class B's "foo", the calling class says …
No, the compiler says it.
… that "foo" is not something of a structured union or a member, which makes me believe it needs to be explicitly synthesized.
It is. In class A.
The compiler is giving you that warning because it doesn't know about the @property, which is because you have neither declared it nor imported a header that declares it. You say that class A's header declares the property, so import class A's header into class B's implementation, so that the compiler knows about the property when compiling class B.