Can I claim my mother and grandfather as dependents?

Probably.

A person can still be a Qualifying relative dependent, if not a Qualifying Child, if he meets the 6 tests for claiming a dependent:

1. Closely Related OR live with the taxpayer ALL year

2. His/her gross taxable income for the year must be less than $4,050 (2016)

3. The taxpayer must have provided more than 1/2 his support

In either case:

4. He must be a US citizen or resident of the US, Canada or Mexico

5. He must not file a joint return with his spouse or be claiming a dependent of his own

6. He must not be the qualifying child of another taxpayer

Social security and food stamps don't count as income, for the income test, but social security & welfare money he/she spends on her self does count as support not provided by you, for the support test. Money she puts into savings & investment does not count as support she spent on herself. Note that a parent and grandparent are closely related so there is no requirement that she live with you at any time, during the year. But if you provided a home it helps your support case, unless they own the home you live in. If no one person (or married couple) provides 50% of the support (for example your siblings are also sending support), then a "multiple support agreement” (IRS Form 2120) can be used, to allow you to claim the dependent.

The IRS has a worksheet that can be used to help with the support calculation. See: http://apps.irs.gov/app/vita/content/globalmedia/teacher/worksheet_for_determining_support_4012.pdf The support value of a home is the fair market rental value, divided by the number of occupants.