Hoi,
Taking excursions math 112 and I was wondering on why in Sets are empty/null sets are assumed subsets of every set? Isn't the definition of a subset meaning a set containing elements of a larger set? So how is it that an empty/null set is a subset of any set?
Ok so I got my answer and I'm going to answer it here just in case someone ever has the same problems/wants this to actually be answered. <.<
The reason ∅ is an applicable answer to all sets is because all problems of sets can have an empty/null set as an answer. The complete absence of elements.
Examples:
You have four police cars you can dispatch, a, b, c, and d.
You can send no cars. ∅
You can send 1 car. {a}, {b}, {c}, {d}
You can send 2 cars. {a,b}, {c,d}, {a,d}, {c,b}, {b,d}, {c,d}
You can send 3 cars. {a,b,c}, {b,c,d} {a,b,d}, {a,c,d}
You can send 4 cards. {a,b,c,d}
You have a hamburger with three available condiments. Ketchup, mayo, and mustard. Combine in anyway you choose.
You can have no condiments. ∅
You can have 1 condiments. {k}, {ma}, {mu}
You can have 2 condiments. {k, ma}, {k, mu}, {ma, mu}
You can have all the condiments you greedy fuck. {k, ma, mu}
Thanks for the help guys. Dam u str8 babygurl have fun.
Sources: mathisfun, Wikipedia, Topics in Contemporary Mathematics