If item $$i$$ is selected, then item $$j$$ is not selected, and the constraint reads: $$x_i + x_j \leq 1$$.
I am confused about the $$\leq$$ sign, because say item $$i$$ is not selected, does that also mean that item $$j$$ is not selected?
This “conflict” constraint prevents selecting both items but allows either item or neither item to be selected. Of the four possibilities for $$(x_i,x_j)$$, only $$(1,1)$$ is excluded.