Question #171722

A. Write each of the following sets by listing their elements between braces.

2. {3x+2:xϵZ}

4. {xϵN:-2<x≤7}

6. {xϵR:x2=9}

8. {xϵR:x3+5x2=-6x}

10. {xϵR:sin πx=0}

B. Write each of the following sets in set-builder notation.

18. {0,4,16,36,64,100,…}

20. {…,-8,-3,2,7,12,17,…}

22. {3,6,11,18,27,38,…}

24. {-4,-3,-2,-1,0,1,2}

26. {…,1/27,1/9,1/3,1,3,9,27,…}

C. Find the following cardinalities.

30. │{{1,4},a,b,{{3,4}},{Ø}}│

32. │{{{1,4},a,b,{{3,4}},{Ø}}}│

34. │{xϵN:│x│<10}│

36. │{xϵN:x2<10}│

38. │{xϵN:5x≤20}│

D. Sketch the following sets of points in the x-y plane.

40. {(x,y):xϵ[0,1],yϵ[1,2]}

42. {(x,y):x=2,yϵ[0,1]}

44. {(x,x2):xϵR}

46. {(x,y):x,yϵR,x2+y2≤1}

48. {(x,y):x,yϵR,x>1}

50. {(x,x2/y):xϵR,yϵN}


1
Expert's answer
2021-03-29T01:42:44-0400

Solution.

A.

2. {3x+2:xZ}={...,4,1,2,5,8,11,14,...}.\{3x+2:x\in Z\}=\{...,-4,-1,2,5,8,11,14,...\}.

4.

{xN:2<x7}={1,0,1,2,3,4,5,6,7}.\{x\in N:-2<x\leq7\}=\{-1,0,1,2,3,4,5,6,7\}.

6.

{xR:x2=9}={3,3}.\{x \in R:x^2=9\}=\{-3,3\}.

8.

{xR:x3+5x2=6x}={3,2,0}.\{x\in R:x^3+5x^2=-6x\}=\{-3,-2,0\}.

10.

{xR:sinπx=0}={...,3,2,1,0,1,2,3,...}.\{x\in R:\sin{πx}=0\}=\{...,-3,-2,-1,0,1,2,3,...\}.

B.

18.

{0,4,16,36,64,100,...}={xZ:(2x)2}.\{0,4,16,36,64,100,...\}=\{x\in Z:(2x)^2\}.

20.

{...,8,3,2,7,12,17,...}={xZ:5x3}.\{...,-8,-3,2,7,12,17,...\}=\{x\in Z:5x-3\}.

22.

{3,6,11,18,27,38,...}={xN:x2+2}.\{3,6,11,18,27,38,...\}=\{x\in N:x^2+2\}.

24.{4,3,2,1,0,1,2}={xZ:4x2}.\{-4,-3,-2,-1,0,1,2\}=\{x \in Z:-4\leq x\leq 2\}.

26.

{...,127,19,13,1,3,9,27,...}={xZ:3x}.\{...,\frac{1}{27},\frac{1}{9},\frac{1}{3},1,3,9,27,...\}=\{x \in Z:3^x\}.

C.

30.

{{1,4},a,b,{{3,4}},{}}=5.|\{\{1,4\},a,b,\{\{3,4\}\},\{\varnothing\}\}|=5.

32.

{{{1,4},a,b,{{3,4}},{}}}=1.|\{\{\{1,4\},a,b,\{\{3,4\}\},\{\varnothing\}\}\}|=1.

34.

{xN:x<10}=9.|\{x\in N:|x|<10\}|=9.

36.

{xN:x2<10}=3.|\{x\in N:x^2<10\}|=3.

38.

{xN:5x20}=4.|\{x \in N:5x\leq 20\}|=4.

D.

40.



42.



44.



46.



48.



50.





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Comments

Abby
06.10.21, 20:27

It's a good help for students like me

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