Just another fairly simple problem. Feel free to let me know if i got myself mixed up.
(;AB[gi]AB[gh]AB[hh]AB[ih]AB[hj]AB[hk]AB[ik]AB[jk]AB[ji]AB[ki]AB[kj]AB[kk]AW[jh]AW[jg]AW[ig]AW[hg]AW[gg]AW[fg]AW[fh]AW[fi]AW[gj]AW[fj]AW[gk]AW[gl]AW[hl]AW[il]AW[jl]AW[kl]AW[kh]AW[lh]AW[li]AW[lj]AW[ll]AW[jj]C[Would white be better off if the marked stone didn't exist?]LB[ii:N]LB[ij:Y]TR[jj]AP[goproblems]
(;W[ii];B[hi]C[Incorrect. Black Lives thanks to his liberty at M9.])
(;W[ij]C[Correct! White could kill were it not for his own stone at K10.RIGHT])
(;W[hi]C[NOTTHIS])
(;W[lk]C[NOTTHIS]))