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Intersection of Subsets

  • Thread starter ragnes
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f: A-->B is a function. A,B are sets.
Let A1, A2 be contained in/equal to A.

f(A1 intersection A2) is contained in OR equal to f(A1) intersection with f(A2). Show that the equality holds if f is an injection.

I know how to prove that it is contained, but not the equal/injection part. Help please!
 

Answers and Replies

  • #2
f: A-->B is a function. A,B are sets.
Let A1, A2 be contained in/equal to A.

f(A1 intersection A2) is contained in OR equal to f(A1) intersection with f(A2). Show that the equality holds if f is an injection.

I know how to prove that it is contained, but not the equal/injection part. Help please!
Okay, so far you have proved that....
[tex] f(A_{1}\cap A_{2}) \subseteq f(A_{1})\cap f( A_{2})[/tex]

When you want to prove equality of sets ( say A and B) you have to show [tex]A\subset[/tex] B and [tex]B \subset A[/tex].

Where in the process of showing equality are you stuck ?
 

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