Adding New Tenants on a Lease

[Grace Carol]

I have a 4-bedroom unit in San Francisco with 4 tenants and 2 of the old tenants moved out and they have asked that I approve new ones to replace the 2 that moved out. Am I obliged to add new tenants, after reviewing their background, or does the lease terminate if one of the tenants move out? There is nothing specific in the lease agreement.

Thanks