Assume that b < d i.e b-d <0 ….(1)

Given that a <c i.e a-c < 0and a+b=c+d

The given equation can be written as

a-c=d-b

We know that a-c <0

Therefore d-b <0 …..(2)

Equation (2) contradicts our assumption

Which implies that our assumption has gone wrong

Therefore d <b