The coroner has instructed the jury that they can return conclusions (previously known as verdicts) of "unlawful killing" on Rachael and Auden Slack, and "suicide" on Andrew Cairns.
Dr Robert Hunter has also told them they can return a narrative conclusion on Miss Slack and Auden which includes mention of unlawful killing either by murder or voluntary manslaughter, depending on their assessment of the state of mind of the person responsible.
The jury, he said, must reach their conclusions "beyond all reasonable doubt".
A Coroner's report has made recommendations after an inquest found Rachael Slack and her son were unlawfully killed by her former partner.
A timeline of the events surrounding the stabbing of Rachael Slack, Andrew Cairns and their two-year old son, Auden.
The inquest on a mentally ill patient found stabbed to death with his ex-partner and their son in Derbyshire will hear further evidence.