SELECT DISTINCT a.id
  FROM a
  JOIN b
    ON a.val=b.val

SELECT a.id
FROM   a
EXCEPT
SELECT a.id
FROM   a
WHERE  a.val NOT IN ( SELECT b.val FROM b )

I'm nut sure I understand what you want to say with this.

I thought that this is a variation of "Relational Division".
B.foo is not necessary the number of B.val of the group.
It can be 'A' and 'B' instead of 3 and 2.
------------------- Commands Entered --------------------
SELECT id, val
 FROM A a1
    , (SELECT DISTINCT foo
         FROM B
      ) b1
WHERE NOT EXISTS
      (SELECT *
         FROM B b2
        WHERE b2.foo = b1.foo
          AND NOT EXISTS
              (SELECT *
                 FROM A a2
                WHERE a2.id  = a1.id
                  AND a2.val = b2.val
              )
      )
ORDER BY
      id, val;
-------------------------------------------------------

ID     VAL
------ ------
    1      3
    1      4
    1      7
    5      8
    5      9

 5 record(s) selected.

If you needed only A.id, following would work.
------------------- Commands Entered --------------------
SELECT a.id
 FROM A
      INNER JOIN
      B b1
        ON a.val = b1.val
GROUP BY
      a.id, b1.foo
HAVING COUNT(a.val)
      = (SELECT COUNT(b2.val) FROM B b2 WHERE b2.foo = b1.foo);
---------------------------------------------------------

ID
------
    1
    5

 2 record(s) selected.

If used a characteristics of original B table design(B.foo is the
number of B.val of the group), query would be slightly simple.
--------------------- Commands Entered -------------------
SELECT a.id
 FROM A
      INNER JOIN
      B b1
        ON a.val = b1.val
GROUP BY
      a.id, b1.foo
HAVING COUNT(a.val) = b1.foo;
----------------------------------------------------------

ID
------
    1
    5

 2 record(s) selected.