Match each geographic tool to its description.

May consider a group  g=({0,1},+)g=({0,1},+)where  ++  will work as the xor operator like we work in boolean algebra. note here, that ‘00’ and ‘11’ are not the usual 0 and 1 that we work with everyday. the elements are  called  ‘00’ and ‘11’ and  may not mean  zero (nothing) and one (single). ‘00’ is the identity for the given binary operator +, meaning that any element operated with ‘00’ gets us that element itself.  for a set  ss  in  g′g′  having more elements than just  {0,1}{0,1}  the values for  a+b∈sa+b∈s, such that  a∈s,b∈sa∈s,b∈s, have to be first defined, only then can you determine the value of  1+11+1. the answer could possibly have been  22  if oanswer is25,000

The investiture controversy began as a power struggle between pope gregory vii (1072–85) and henry iv, holy roman emperor (1056–1106).[2] a brief but significant struggle over investiture also occurred between henry i of england and pope paschal ii in the years 1103 to 1107, and the issue played a minor role in the struggles between church and state in france, as well.by undercutting the imperial power established by the salian emperors, the controversy led to nearly 50 years of civil war in germany, and the triumph of the great dukes and abbots. imperial power was finally re-established under the hohenstaufen dynasty. historian norman cantor: