1. Though both sec 24(b) and 10(13A) are different and operate independently. The practical scenario in most of the cases is that they would be having a house property and repaying the loan on the same and stay in another house and claim HRA exemption u/s 10(13A)
2. The important point is both the above section operates exclusively and one is in no way operates with other. Hence, if an assesse as long as he satisfies the conditions for claiming HRA u/s 10(13A) ( by staying in a rented house other than his own house ) he can avail the benefit.
3. With respect to housing loan repayment ( principal and interest ), the same can be availed as long as the conditions attached to it is fullied. If the rent received on house is shown under Income from house property, interest paid on the same can be availed and the same will be considered as cost while computing capital gains.
4. So both sections operate separately and the assessee can be benefitted.
Yes. both can be very much claimed.