Posting personal information such as your birth date, family member names, and home address, does not increase your risk of identity theft.

The answer is false. It increases your chances of identity theft. In identity theft fraud, the thief uses your name, private information, and credit to take products and services and leaves you holding a bag of troubles. They get information through the following:
Stealing Mail, wallet or purses
Sending a change of address
Soliciting account information over the phone
Accessing personal information you share on the Internet
Using fake websites to get your personal information
Posing as a person with legitimate access to your credit report.