Is {a^i b^j c^k | i≤j or (k=j≤i)} context sensitive?
There are two possible interpretations of the condition on $i,j,k$:


$(i \leq j \lor j \leq i) \land j = k$. This condition is equivalent to just $j = k$, and so the language in question is $\{ a^i b^j c^j : i,j \geq 0 \}$, which is a prototypical context-free language.
$i \leq j \lor (j \leq i \land j = k)$. A linear-bounded automaton can decide this language (exercise), so it is context-sensitive. On the other hand, using the pumping lemma you can show that it is not context-free (exercise).


I would guess that the second interpretation is the one that was intended.