Question

Help with equivalence relations and partial orders.

Answer 1

I can think of many examples for the other way around, but not for that... :/

Answer 2

What is the two definitions?

Answer 3

Well for partial order, you need anti-symmetry. For equivalence you just need symmetry. But both need reflexive and transitive.

Answer 4

hint: think subsets

Answer 5

does \(A\subset B \) imply \( B \subset A\)?

Answer 6

Not unless they are equal.

Answer 7

ps I made another comment on your last post

Answer 8

correct

Answer 9

oh kk, i'll go look at it! thakn you!

Answer 10

so subset inclusion is a partial order and not a equivalence relation

Answer 11

OO, that makes sense! and when it says define the universal set, what does that mean?

Answer 12

just pick a set like \(\mathbb{N}\)

Answer 13

so the universal set would be \(P(\mathbb{N})\) (The set of all subsets of \(\mathbb{N}\))

Answer 14

ooo! gotchya gotchya thanks!

Answer 15

np