Which are skew lines? check all that apply

a and b
c and b
b and e
e and c
a and e
a and c

2 lines are skew if they are neither parallel, nor intersecting.

If 2 lines are parallel or intersecting, they form a plane, so they are coplanar. So "skew" is the opposite or complement  of "coplanar".

i) a and b: are both on M so coplanar, not skew

ii) b is in M, c is in N and they have no common point, so skew. (if they had a common point that would be a point in the line d of intersections of planes M and N, but they dont meet at such a point)

iii) b and e: are both on M so coplanar, not skew

iv) e and c : skew, same argument as ii. 

v) a and e : are both on M so coplanar, not skew

vi) a and c: a is in M, c is in N. If they met, they would met at a point on line d, the only set of points common to planes M and N, but they dont. so skew