Solution Found!
Let f be a function from A to B. Let S and T be subsets of
Chapter 1, Problem 44E(choose chapter or problem)
Let \(f\) be a function from \(A\) to \(B\). Let \(S\) and \(T\) be subsets of \(B\). Show that
a) \(f^{-1}(S \cup T)=f^{-1}(S) \cup f^{-1}(T)\).
b) \(f^{-1}(S \cap T)=f^{-1}(S) \cap f^{-1}(T)\).
Equation Transcription:
.
Text Transcription:
f
A
B
S
T
f^−1(S cup T)=f^−1(S) cup f^−1(T) .
f^−1(S cap T)=f^−1(S) cap f^−1(T)
Questions & Answers
QUESTION:
Let \(f\) be a function from \(A\) to \(B\). Let \(S\) and \(T\) be subsets of \(B\). Show that
a) \(f^{-1}(S \cup T)=f^{-1}(S) \cup f^{-1}(T)\).
b) \(f^{-1}(S \cap T)=f^{-1}(S) \cap f^{-1}(T)\).
Equation Transcription:
.
Text Transcription:
f
A
B
S
T
f^−1(S cup T)=f^−1(S) cup f^−1(T) .
f^−1(S cap T)=f^−1(S) cap f^−1(T)
ANSWER:
Solution:
Step 1 :
In this problem we have to the prove the following properties.
Let and
and
be subset of
Then prove that