Let $I$ and $J$ be two monomial ideals of $R=K[x_1,\dotsc,x_n]$ where $K$ is a field.

Could we say $\operatorname{depth} (R/I)\leq \operatorname{depth}(R/(I:J))$, where $(I:J)$ is colon ideal and $I\nsubseteq J$?

Let $I$ and $J$ be two monomial ideals of $R=K[x_1,\dotsc,x_n]$ where $K$ is a field.

Could we say $\mid\operatorname{depth} (R/I)- \operatorname{depth}(R/(I:J))\mid\leq 1$, where $(I:J)$ is colon ideal and $I\nsubseteq J$?

Let $I$ and $J$ be two monomial ideals of $R=K[x_1,\dotsc,x_n]$ where $K$ is a field.

Could we say $\operatorname{depth} (R/I)\leq \operatorname{depth}(R/(I:J))$, where $(I:J)$ is colon ideal?

Let $I$ and $J$ be two monomial ideals of $R=K[x_1,\dotsc,x_n]$ where $K$ is a field.

Could we say $\operatorname{depth} (R/I)\leq \operatorname{depth}(R/(I:J))$, where $(I:J)$ is colon ideal and $I\nsubseteq J$?

Let $I$ and $J$ be two monomial ideals of $R=K[x_1,\ldots,x_n]$ where $K$ is a field.

Could we say $\operatorname{depth} (R/I)\leq \operatorname{depth}(R/(I:J))$, where $(I:J)$ is colon ideal?

Let $I$ and $J$ be two monomial ideals of $R=K[x_1,\dotsc,x_n]$ where $K$ is a field.

Could we say $\operatorname{depth} (R/I)\leq \operatorname{depth}(R/(I:J))$, where $(I:J)$ is colon ideal?