How many people in our house are exempt from CT

[Brahma56]

Six months ago, the health of my 90-year old mother deteriorated and she became unable to live alone. My partner and I gave up the lease on our flat and together with my mother took out a lease on a larger property so that we could care for her. Because Mum receives the guaranteed element of Pension Credit, she also receives full relief of her council tax liability. As I provide in excess of 60 hours per week care I should be exempt from CT, leaving my partner as the only person liable to pay. That as I understood it should have resulted in a 25% reduction in her liability. However, the local authority says that Mum receives full support and I am exempt, but my exemption does not apply because there are still two liable payees in the house, Mum and my partner. Can this be right?