In SQL SERVER it is BIT , though it allows NULL to be stored

ALTER TABLE person add  [AdminApproved] BIT default 'FALSE';

Also there are other mistakes in your query

1. When you alter a table to add column no need to mention column keyword in alter statement
2. For adding default constraint no need to use SET keyword
3. Default value for a BIT column can be ('TRUE' or '1') / ('FALSE' or 0) . TRUE or FALSE needs to mentioned as string not as Identifier

The answer given by Pரதீப் creates a nullable bool, not a bool, which may be fine for you. For example in C# it would create: bool? AdminApproved not bool AdminApproved .

If you need to create a bool (defaulting to false):

ALTER TABLE person
    ADD AdminApproved BIT
    DEFAULT 0 NOT NULL;

In phpmyadmin, If you need to add a boolean datatype column to an existing table with default value true:

ALTER TABLE books
   isAvailable boolean default true;

There are two ways that you can do it.

ALTER TABLE `tablename`
ADD `column_name` BOOLEAN DEFAULT FALSE 

ALTER TABLE `tablename`
ADD `column_name` TINYINT DEFAULT 0