# Math Help - Question on Function Proof

1. ## Question on Function Proof

(it is a prep question for the qualifier and taken from an old exam)

Assume a function f: A->B and sets A1, A2 $\subseteq$ A, for which f(A1 $\cap$ A2) $\neq$ f(A1) $\cap$ f(A2).
Demonstrate this inequality.

2. Originally Posted by itpro
Assume a function f: A->B and sets A1, A2 $\subseteq$ A, for which f(A1 $\cap$ A2) $\neq$ f(A1) $\cap$ f(A2).
Demonstrate this inequality.
$A=\{1,2\},~B=\{a,b\}~\&~f=\{(1,b),(2,b)\}.$

$A_1=\{1\}~\&~A_2=\{2\}$ then $f(A_1\cap A_2)=?$.

$f(A_1)\cap f(A_2)=?$