There is no woman slicing an onion. 
A woman is slicing an onion.

Every European can travel freely within Europe
Every European can travel freely.
Every happy European can travel freely within Europe.

A group of scouts are hiking through the grass.
Some people are walking.

A man, a woman and two girls are walking on the beach.
Four people are walking on the beach.

Romano Prodi will meet the US President George Bush in his capacity as the president of the European commission.
George Bush is the president of the European commission.
Romano Prodi is the president of the European commission.

Romano Prodi will meet the US President George Bush in their capacities as presidents of big institutions.
George Bush is the president of a big institution.
Romano Prodi is the president of a big institution.