Mapping/Take preimage/Exercise

Let ${}F\colon L\rightarrow M$ denote a mapping. Show that taking preimages

${\mathfrak {P}}\,(M)\longrightarrow {\mathfrak {P}}\,(L),T\longmapsto F^{-1}(T),$

fulfills the following properties (for arbitrary subsets ${}T,T_{1},T_{2}\subseteq M$):

1. ${}F^{-1}(T_{1}\cap T_{2})=F^{-1}(T_{1})\cap F^{-1}(T_{2})\,,$

2. ${}F^{-1}(T_{1}\cup T_{2})=F^{-1}(T_{1})\cup F^{-1}(T_{2})\,,$

3. ${}F^{-1}(M\setminus T)=L\setminus F^{-1}(T)\,.$

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