- #1

tomboi03

- 77

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_{i}[tex]\subset[/tex] A and B

_{i}[tex]\subset[/tex]B for i=0 and i=1. Shwo that f

^{-1}preserves inclusions, unions, intersections, and differences of sets:

a. B

_{0}[tex]\subset[/tex]B

_{1}= f

^{-1}(B

_{0})[tex]\subset[/tex]f

^{-1}(B

_{1})

b. f

^{-1}(B

_{0}[tex]\cup[/tex]B

_{1}) = f

^{-1}(B

_{0})[tex]\cup[/tex]f

^{-1}(B

_{1})

c. f

^{-1}(B

_{0}[tex]\cap[/tex]B

_{1}) = f

^{-1}(B

_{0})[tex]\cap[/tex]f

^{-1}(B

_{1})

d. f

^{-1}(B

_{0}-B

_{1}) = f

^{-1}(B

_{0})-f

^{-1}(B

_{1})

Show that f preserves inclusions and unions only:

e. A

_{0}[tex]\subset[/tex]A1

_{1}=> f(A

_{0})[tex]\subset[/tex]f(A

_{1})

f. f(A

_{0}[tex]\cup[/tex]A

_{1})=f(A

_{0})[tex]\cup[/tex]f(A

_{1})

g.f(A

_{0}[tex]\cap[/tex]A

_{1})=f(A

_{0})[tex]\cap[/tex]f(A

_{1}); show that equality holds if f is injective

h.f(A

_{0}-A

_{1})=f(A

_{0})-f(A

_{1}); show that equality holds if is injective

Thanks