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* Properties of Countable seb:-, The set of all R between OfI in uncountaby., 03o-ム, to, or 0.5 0. 75 I, 0.01, © Any subset of any countuble set is countable,, A={ 1,2,3,....- 9}, B = { 2,4,6,83, ニ, BS A, Courntabl. Countable., set with uncountable subset i uncountable., Any, BS A, Uncountabt, 8={0,2,4,6, 8,-, 100, 102, - -o00,1000, A={-0 -3-2-1, 0, 1, 2,3,, Uncountable, © Any infinite set contrins a, countably infinite, subjet
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O A disjoint union of finite set f, infinite set s, Countably infinite ., any, any. countably, O Union of any teso countably imfinite seb, is countabaly infinite., A Union of any, two countable set » Countalble, O Set of all integen is countable., Nx N. ;>, Countable. N Natural 1b., Q] Prove that, Any set with an uncountable subset, is uncountabk., A let, s, f A be a subset of s., be, any, set., let, s be courtable set. then by, Poo perty i e. Any subset f'any, Cauntable set is countable., .A is countabl., s is countable, A is countable., By law A ontrapositive. (pig= ng-sap), (2), Ais uncountable=s !, is unlountd
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is countable, ges., 3-13,, si7,-., -6,-4,-20,2, 4,6, 8,, a let, I be a set of all Integen., 4 E be a set of all even, inntegen, Also, O be a set A all odd integens, ' EC Z, こう0, Z={...- -3,-2,-1,0, 1, 2, 3, . ...}, E = 4.-.. -2, 0, 2,4, - - -- }, O= Ź - -..-3,-1, 1,3, - - -- }, -2,0, 2,4,-, :' Set of all Integen. is countable., y poperty), f subset of Countable? countabl., --(By pooperty), fodd integens, set d all even ,, Courntable., H.P.
