a) Consider a subset X = {2, 4, 5, 7, 8, 9, 10, 21} of the...

 

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a) Consider a subset X = {2, 4, 5, 7, 8, 9, 10, 21} of the set of natural numbers N. Define an order relation <' on N by m <n m|n for m, n E N. (Recall that m | n when n = mk for some k E N). i) Find all the maximal and minimal elements of (X, <). ii) Find the supremum and infimum of X. b) Let X andY be sets. Prove that X is equipotent to a subset of Y if and only if there exists an injective function f : X Y. [4,3,8] a) Consider a subset X = {2, 4, 5, 7, 8, 9, 10, 21} of the set of natural numbers N. Define an order relation <' on N by m <n m|n for m, n E N. (Recall that m | n when n = mk for some k E N). i) Find all the maximal and minimal elements of (X, <). ii) Find the supremum and infimum of X. b) Let X andY be sets. Prove that X is equipotent to a subset of Y if and only if there exists an injective function f : X Y. [4,3,8]