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1. If a person's only income is social security, it is not taxable and a return does not need to be filed unless tax was withheld and the person wants it refunded.  

 

2. On the other hand, if a person has other taxable income in their own name (IRA, pension, gambling winnings, etc.) they must file a tax return in their own name even if they are also someone else's dependent.

 

3. Your sister can't claim your mother as a dependent if your mother has more than $4300 of taxable income (for 2021.  I don't know the amount for 2022 but it will be a little higher.)

 

4. Even if your mother has less than $4300 of taxable income and can be claimed as a dependent by your sister, she is not a qualifying person for HOH unless she also lived in your sister's home more than half the year.