this is really good question
A)There are topologies and link costs where the majority of the routes to other nodes will be incorrect. True
Here professor connected u to v1 & v2 & v3 as they are directly connected to u.
but what if there is edge between v1 and v2 having weight 1
also what if there is edge between v1 and v3 having weight 1
then above topology will be wrong.
B)There are topologies and link costs where no routing table entry (other than from u to itself) will be correct. False
professor Ram connecting u to all its connected vertices(suppose there are n such vertices ). And at later stage even if we discovered that out of n connected vertices of u , n-1 have better path. but still there will be 1 vertices which is correctly connected to u. Otherwise u will not be connected at all
Lets take above figure only
in that we discovered better path from u to v2 & from u to v2. But still entry u to v1 has not change.
Hence there will be atleast one correct entry.
C)There are topologies and link costs where all routing table entry (other than from u to itself) will be correct. True
Consider above graph only and assume that apart from edges shown in figure no other edge exist.
Please reply if you think anything incorrect