Unfortunately I have no idea how to show this:Show that the set of ${\sf P}$-complete languages is not closed under intersection.As far as I understand my lecture notes, ${\sf P}$-completeness is defined as follows:$A \subset \Sigma^{*}$ is complete for ${\sf P}$ iff $A \in \text{P}$ and $\forall B \in {\sf P}, B \le_L A$$\le_L$ is ${\sf LOGSPACE}$-reduction: for $A,B \subset \Sigma^{*}$, the relation $A \le_{L} B$ is defined by$$A \le_{L} B \quad\text{iff}\quad \exists f \in {\sf FLOGSPACE}, (x \in A \Leftrightarrow f(x) \in B)$$
Proof for P-complete is not closed under intersection
complexity theory;time complexity;reductions