Create a new column by comparing set of column values

How can I group a set rows by 'product_id' from a table and create a new column by comparing a set of column values within the group ?

For example,

product id   part_id  availability
1            1        true
1            2        false
1            3        true
2            1        true
2            4        true
2            8        true

By comparing the 'availability',I would like to create a 'feasibility' column. If single part is missing it would't be feasible.

product_id  feasibility
1           false
2           true

I used GROUP BY clause to sort'em out by product_id but I can't figure out the second part.