In Jech's Intro. to Set Theory Problem 2.3 f
$R^{-1}[R[A]] \supseteq A \cap dom R $. Can I say that $R^{-1}[R] $ should be the identity relation and hence the above simplifies to $A \supseteq A \cap dom R$ which is true.
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$R^{-1}[R]$ contains the identity relation. It doesn't have to be equal to the identity relation. See exercise $2.4(e)$. – quasi Mar 19 '17 at 09:21
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yes just saw that question thanks for pointing that out – arrhhh Mar 19 '17 at 09:30
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But exercise $2.3(f)$ is straightforward. Take an element $a \in A \cap \text{ dom } R$, and show that it's in $R^{-1}[R[A]]$. – quasi Mar 19 '17 at 09:39
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yes I didn't know that that was the method I needed to follow, had to look at a solution for that – arrhhh Mar 19 '17 at 11:31