Consider the set A := {1, 2, . . . , n}. Consider the following claim: there exists a relation on the set A that is both an equivalence relation and a partial order. Either prove that the claim is...

Consider the set A := {1, 2, . . . , n}. Consider the following claim: there exists a relation on the set A that is both an equivalence relation and a partial order. Either prove that the claim is true (and describe, as precisely as possible, the structure of any such relation ) or disprove the claim.