TRUE and FALSE are keywords, and should not be quoted as strings:
INSERT INTO first VALUES (NULL, 'G22', TRUE);
INSERT INTO first VALUES (NULL, 'G23', FALSE);
By quoting them as strings, MySQL will then cast them to their integer equivalent (since booleans are really just a one-byte INT in MySQL), which translates into zero for any non-numeric string. Thus, you get 0 for both values in your table.
Non-numeric strings cast to zero:
mysql> SELECT CAST('TRUE' AS SIGNED), CAST('FALSE' AS SIGNED), CAST('12345' AS SIGNED);
+------------------------+-------------------------+-------------------------+
| CAST('TRUE' AS SIGNED) | CAST('FALSE' AS SIGNED) | CAST('12345' AS SIGNED) |
+------------------------+-------------------------+-------------------------+
| 0 | 0 | 12345 |
+------------------------+-------------------------+-------------------------+
But the keywords return their corresponding INT representation:
mysql> SELECT TRUE, FALSE;
+------+-------+
| TRUE | FALSE |
+------+-------+
| 1 | 0 |
+------+-------+
Note also, that I have replaced your double-quotes with single quotes as are more standard SQL string enclosures. Finally, I have replaced your empty strings for id with NULL. The empty string may issue a warning.
0and1as values for insert such that it is explicitly clear what you are trying to do in the code (i.e. not depending on casting behavior)