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Preserves inclusions, unions intersections

  1. Feb 2, 2009 #1
    Let f: A-> B and let Ai[tex]\subset[/tex] A and Bi[tex]\subset[/tex]B for i=0 and i=1. Shwo that f-1 preserves inclusions, unions, intersections, and differences of sets:
    a. B0[tex]\subset[/tex]B1 = f-1(B0)[tex]\subset[/tex]f-1(B1)
    b. f-1(B0[tex]\cup[/tex]B1) = f-1(B0)[tex]\cup[/tex]f-1(B1)
    c. f-1(B0[tex]\cap[/tex]B1) = f-1(B0)[tex]\cap[/tex]f-1(B1)
    d. f-1(B0-B1) = f-1(B0)-f-1(B1)

    Show that f preserves inclusions and unions only:
    e. A0[tex]\subset[/tex]A11 => f(A0)[tex]\subset[/tex]f(A1)
    f. f(A0[tex]\cup[/tex]A1)=f(A0)[tex]\cup[/tex]f(A1)
    g.f(A0[tex]\cap[/tex]A1)=f(A0)[tex]\cap[/tex]f(A1); show that equality holds if f is injective
    h.f(A0-A1)=f(A0)-f(A1); show that equality holds if is injective

  2. jcsd
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