# Total ordering and relations set theory problem?

Orderings and relations - set theory?

Find counter-examples to prove that none of the relations of

divisibility on Z,

equality on S,

containment on P(S) (power set)

is a total ordering

any ideas?

Find counter-examples to prove that none of the relations of

divisibility on Z,

equality on S,

containment on P(S) (power set)

is a total ordering

any ideas?

Update:
sorry, given set S,

s,t are an element of S

define s is related to t if s = t

s,t are an element of S

define s is related to t if s = t

Update 2:
for P(S)

given A,B are elements of P(S),

A is related to B if A is a proper subset of B

given A,B are elements of P(S),

A is related to B if A is a proper subset of B

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