Why am I getting `Impossible WHERE noticed after reading const tables` in explain query?

You are getting the message

Impossible WHERE noticed after reading const tables

This is documented in the page you already linked.

MySQL has read all const (and system) tables and notice that the WHERE clause is always false

const tables are defined as

The table has at most one matching row, which is read at the start of the query. ... const is used when you compare all parts of a PRIMARY KEY or UNIQUE index to constant values.

You have a UNIQUE KEY on (fromid,toid). The query on WHERE fromid=78 AND toid=60 can be satisfied by reading this unique index. From the message you are getting this must return no results.

Similarly the query WHERE fromid=60 and toid=78 AND (is_approved='s' OR is_approved='f' OR is_approved='t') can also use this index to locate the row of interest (though it still has a residual predicate to evaluate were any row to match).

Your other query is different

SELECT rid
FROM   relationship
WHERE  fromid = 60
       AND toid = 78
       AND is_approved = 's'
        OR is_approved = 'f'
        OR is_approved = 't' 

AND has a higher precedence than Or, so this is the same as

SELECT rid
FROM   relationship
WHERE  ( ( fromid = 60 ) AND ( toid = 78 ) AND ( is_approved = 's' ) )
        OR ( is_approved = 'f' )
        OR ( is_approved = 't' ) 

This can no longer use that index and has different semantics in that it will return any rows where is_approved IN ('f','t') irrespective of what the values in the other columns are.

MySql Explain uses the values you provide, literally, to traverse rows of the associated tables. If you provide a constant/key value which is not in the associated table, MySql Explain will stop with this error. Simply query the associated table(s) for values which do exist and provide those in your Explain query and everything will work as expected.

Impossible WHERE noticed after reading const tables in explain query?

This error occurs due to invalid value being put on a column which are either primary key or unique key.

Try with a correct value in the where clause .