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}
Solution.
A.
2.
4.
6.
8.
10.
B.
18.
20.
22.
24.
26.
C.
30.
32.
34.
36.
38.
D.
40.
42.
44.
46.
48.
50.
Comments
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