Several inequalities regarding sdepth

We give several bounds for $sdept{h}_S(I+J)$, $sdept{h}_S(I\cap J)$, $sdept{h}_S(S\mathrm{/}(I+J))$, $sdept{h}_S(S\mathrm{/}(I\cap J))$, $sdept{h}_S(I:J)$ and $sdept{h}_S(S\mathrm{/}(I:J))$ where $I,J\subset S=K[x_1,\mathrm{.}\mathrm{.}\mathrm{.},x_n]$ are monomial ideals. Also, we give several equivalent forms of Stanley Conjecture for $I$ and $S\mathrm{/}I$, where $I\subset S$ is a monomial ideal.