# Set Theory

• January 25th 2007, 10:36 AM
taypez
Set Theory

Given f: X maps to Y with A1, A2 c X and B1, B2 c Y

which of the following are true. Can someone also provide a brief reason why?

1) f(A1 n A2) = f(A1) n (f(A2)

2) f ^-1(B1 n B2) = f^-1(B1) n F^-1 (B2)

3) f ^-1(B1 u B2) = f^-1(B1) u F^-1 (B2)

Thanks
• January 25th 2007, 12:34 PM
Plato
Part a is false. The sets $A_1$ and $A_2$ may be have an empty intersection but their images may overlap.

Parts b & c are true. Can you prove then?