How to use  or != operator
You can use the exists condition to check for the existence of a record through a subquery. This is often preferable to an anti join (a left join where we make sure the right table is null) as the engine stops as soon as it finds a record.

Sample code:

select
    category._id,
    category.cat_name
from
    category
where
    not exists(
        select
            *
        from
            deptcat
            inner join department on(
                department._id = deptcat.dept_id
            )
        where
            deptcat.cat_id = category._id
            and department._id = 1
    )