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A mum and two sons whose bodies were found at their home in Pudsey in Leeds on Sunday suffered stab wounds.
Clair Smith, 36, and her sons Ben, nine, and Aaron, one, were found at their house in Sheridan Way in Pudsey along with thier dad Richard Smith, 37,after concerned relatives raised the alarm.
Richard Smith died as a result of smoke inhalation.
Detective Superintendent Paul Taylor, of West Yorkshire Police, said Mrs Smith died from a single stab wound to her chest, as did baby Aaron.
Ben suffered a stab wound to the chest area but died as a result of suffocation.
In a police briefing Detective Superintendent Paul Taylor said "My thoughts go out to the family and friends of the Smith family.
"I cannot begin to imagine what they have been through during the last 48 hours and the sympathy of the enquiry team rests with them at this time of year.
"As we have previously stated we are not looking for anyone else in connection with this enquiry and our role is to now establish the facts leading up to the tragic event that has ended the lives of four people and a seemingly happy family.
"That information is then passed to the coroner, who will make a decision around the circumstances of the deaths."
Clair Smith and her parents Alan and Norma Robinson paid tribute:
Clair was an exceptional person, loving and caring to everyone. She was a loving mum, her children were her life, and everything centred around her family and home. She was our daughter and our best pal. We cannot imagine what caused this tragedy.