Correct answer => C)
why ?
I) This is false. Consider a system with m < n, which are incosistent like
a+b+c = 2
a+b+c = 3
Here m < n but no solution because of inconsistency !
II) m > n but no solution for none of system => What if this system of equations have 2 equations which are dependent ?
ex => a+b = 2
2a + 2b = 4
a-b = 0
Then a = 1, b= 1 is solutions . II) Is false.
III) this is true, M = 2, N = 2
a+b = 2
a-b = 0
Then m= 1, n= 1 Now there exists system which has solution . III) is correct. Answer is C !