Please help Solve all parts. Note: for c) and d), to prove countable, we requires anexample of a bijection

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Please help Solve all parts.
Note: for c) and d), to prove countable, we requires anexample of a bijection

Please Help Solve All Parts Note For C And D To Prove Countable We Requires Anexample Of A Bijection 1 (25.27 KiB) Viewed 17 times

(a) Justify each of the following properties of If (1.0) and (y, 2) are any two distinct pairs in then either (a,b) <(0,2) or (v.) < (a,b) but not both. (ii) If (a,b), (8,4) and (3, 2) are any three pairs in NF with (0.6) < (3,9) and (p.9) < (y, 2) then (a,b) < (y,2). (This property is known as transitivity) (b) Properties () and (ii) above mean that is a full order. According to this <-order the least", or first pair in N is p = (1.1) and the next is P2 = (1.2). Write out the next eighteen pairs ---Pin this sequence. P1 = (1,1) P2 = (1.2) PS P4= Pe = P = P12 Pis P4= Pisa PG PIR Pa = Pie= (e) Explain why this ordering of N by shows that N is countable. (t.e. N has the same cardinality as N). (d) Is N countable? Justify your answ answer.