The Python version of this exercise has an explanation of the issues involved in taking the symmetric difference of more than two sets. It might be useful to include some of it for the Julia exercise as well (apologies for the Python-only example):
A symmetric difference of more than two sets will result in a set
that includes both the elements unique to each set
AND elements shared between more than two sets in the series (details in the Wikipedia article on symmetric difference).
To obtain only items unique to each set
in the series, intersections between all 2-set combinations need to be aggregated in a separate step, and removed:
>>> one = {'black pepper','breadcrumbs','celeriac','chickpea flour',
'flour','lemon','parsley','salt','soy sauce',
'sunflower oil','water'}
>>> two = {'black pepper','cornstarch','garlic','ginger',
'lemon juice','lemon zest','salt','soy sauce','sugar',
'tofu','vegetable oil','vegetable stock','water'}
>>> three = {'black pepper','garlic','lemon juice','mixed herbs',
'nutritional yeast', 'olive oil','salt','silken tofu',
'smoked tofu','soy sauce','spaghetti','turmeric'}
>>> four = {'barley malt','bell pepper','cashews','flour',
'fresh basil','garlic','garlic powder', 'honey',
'mushrooms','nutritional yeast','olive oil','oregano',
'red onion', 'red pepper flakes','rosemary','salt',
'sugar','tomatoes','water','yeast'}
>>> intersections = (one & two | one & three | one & four |
two & three | two & four | three & four)
...
{'black pepper','flour','garlic','lemon juice','nutritional yeast',
'olive oil','salt','soy sauce', 'sugar','water'}
# The ^ operation will include some of the items in intersections,
# which means it is not a "clean" symmetric difference - there
# are overlapping members.
>>> (one ^ two ^ three ^ four) & intersections
{'black pepper', 'garlic', 'soy sauce', 'water'}
# Overlapping members need to be removed in a separate step
# when there are more than two sets that need symmetric difference.
>>> (one ^ two ^ three ^ four) - intersections
...
{'barley malt','bell pepper','breadcrumbs', 'cashews','celeriac',
'chickpea flour','cornstarch','fresh basil', 'garlic powder',
'ginger','honey','lemon','lemon zest','mixed herbs','mushrooms',
'oregano','parsley','red onion','red pepper flakes','rosemary',
'silken tofu','smoked tofu','spaghetti','sunflower oil', 'tofu',
'tomatoes','turmeric','vegetable oil','vegetable stock','yeast'}