As a cash basis taxpayer, Mary must report the rent collected in December 2018 for January 2019 in her 2018 gross income, making the statement false.
The statement that the amount collected in December 2018 for the 2019 rent should be included in Mary's 2019 gross income is false. As a cash basis taxpayer, Mary must report income in the year she receives it. Therefore, any rent received in December 2018, even if it is for January 2019, should be included in her gross income for the year 2018.