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How to union queries from the same table in MySQL

I have two sets of results:

SELECT name, count(appearance) as countA from table where results = '1'
SELECT name, count(appearance) as countB from table where results = '2'

And I wanted to combine them side by side, like this:

+---------+---------+---------+
| col_1   | countA  | countB  |
+---------+---------+---------+
| John    |    3    |    1    |
| Mary    |    1    |    2    |
| Gary    |    2    |   NULL  |
| Sean    |    4    |   NULL  |
| Mike    |  NULL   |    6    |
+---------+---------+---------+

How do I do that?

This should do it (in Oracle) without needing a self join

SELECT name
     , sum( case results when '1' then 1 else 0 end ) as countA 
     , sum( case results when '2' then 1 else 0 end ) as countB
  from table 
 where results IN ( '1', '2' )
 group by
       name

You could use a self join as follows

select a.col_1, a.countA, b.countB from table a, table b
where a.col_1 = b.col_1 and a.results='1' and b.results='2'
SELECT name, count(appearance) as countA, null AS countB from table where results = '1'
UNION ALL
SELECT name, null AS countA, count(appearance) as countB from table where results = '2'
SELECT `table`.name, countA, countB
FROM tab
LEFT OUTER JOIN
  (SELECT name, count(appearance) as countA from `table` where result = '1' group by name) as tmp1
ON `table`.name = tmp1.name
LEFT OUTER JOIN
  (SELECT name, count(appearance) as countB from `table` where result = '2' group by name) as tmp2
ON `table`.name = tmp2.name;

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