I have an adult living with me but I pay all the bills, he gets social security disability can I claim him and can I claim head of household

It depends. 

Click here for this Interactive Tax Assistant from the IRS: Whom May I Claim as a Dependent?

This article is about Rules for Claiming a Dependent on Your Return, which is about the rules for claiming qualifying children or relatives. Do not worry about the word relative. 

Qualifying relative

Many people provide support to their aging parents. But just because you mail your 78-year-old mother a check every once in a while doesn’t mean you can claim her as a dependent. Here is a checklist for determining whether your mom (or other relative) qualifies.

• Do they live with you? Your relative must live at your residence all year or be on the list of “relatives who do not live with you” in Publication 501. About 30 types of relatives are on this list.
• Do they make less than $4,200 in 2019? Your relative cannot have a gross income of more than $4,200 in 2019 and be claimed by you as a dependent.
• Do you financially support them? You must provide more than half of your relative’s total support each year.
• Are you the only person claiming them? This means you can’t claim the same person twice, once as a qualifying relative and again as a qualifying child. It also means you can’t claim a relative—say a cousin—if someone else, such as his parents, also claim him.