Question

(O)(w) Give the size of each set and also whether it is discrete or continuous. If the set is infinite, determine if it is countably infinite or not. a. A = {seven-digit numbers} b. B = {r: 2x = 1} c. C = {3:0 <r<1 and 1/2 <r <2} d. D = {(x,y): x2 + y2 = 1}

Answer 1

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Answer: (a) A „,9999999 > А { Seren digit numbers} 5) $1000,000 , 1000,00 1, 1,000,0 02, So A is discrete bes values belonging to the set are distinct separate size of 8,999,999 B = {x: 22=1} Şx: x = 1/2 } discrete set (takes only one value) size B (b) - 1 (C) C: {x: 0sxs1 and <<<<2} {x: ut[0,1] and xe ['3,2] c= {x: x{ [0, 1] (97,2]} {x; x+[1791] } c is continuous set, bes x takes every size c = uncountable {bes closed inteirad SR is tencountable) raluce between > 1 and 1. (d) Diş (2,4) : x+y=1} D = {(x, y): unit circle} D is continuous set, it takes each value disk, and cancountable. on unit CS Scanned with CamScanner

(e) E= { x: +34 +2=0} = $x: x be?+27 + x+2-04 x = x (x + 2) +1(8+2) = 0} $x: R + 1)(x+2) = 0; { x: x=-1, x = -2} Discrete Set since takes only two values se=12-2 sire af E = nog elements in Es = 2 2 ) لح F = { positive even integers} {an, nezt § 2, 4, 6, 8, f is discrete bo values bel belongs to dne set are distinct & separate af f & Ze (set of integer) which is countable. F is countable ic CS Scanned with CamScanner