This exercise says:
Let $$p: M \rightarrow N$$ be a $C^s$ map and $$f: N \rightarrow M$$ a $C^r$ section of $p\ $ (i. e. $p \circ f = id_{N}$). Then we need to show:
If $$1 \le r < s \le \infty,$$ then $f$ can be $C^r$ appoximated by $C^s$ sections.
About this exercise, what I think is to do the similar argument as in theorem 2.7, that is in Theorem 2.6, it shows $C^s(M, N)$ is dense in $C_S^r(M,N)$ (subscript $S$ denoted strong topology), then we only need to show sets of section is open in $C_S^r(M, N)$, then we are done, but i don't think we can achieve this, because once in case $M = N$, $p = id_M, f = id_M$, then any perturb of $f$ will not satisfy condition of section $p \circ f = id_M$, I am really confused on this exercise now, can anyone help me about this exercise?