Propositional tableaux again

Test by means of formal tableaux whether the following syntactic sequents are correct:

1. P $\vdash$ [Q $\rightarrow$ [P $\wedge$ Q]]
2. [P $\rightarrow$ Q],[P $\rightarrow$ R],$\neg$[P $\rightarrow$ [Q $\wedge$ R]] $\vdash$
3. $\vdash$ [[[P $\wedge$ Q] $\vee$ [P $\wedge$ R]] $\leftrightarrow$ [P $\wedge$ [Q $\vee$ R]]]