Which should be done in SQL with 1 query.
With sub-query support in your version
$query = "SELECT * FROM (SELECT * FROM tblmembers WHERE emgolf = 'yes' OR emtennis = 'yes' OR emswimming = 'yes' OR emsocial = 'yes') AS t WHERE membernumber like '1%' OR membernumber like '4%' OR membernumber like '9%'";
Couls also use the sub-query in the WHERE clause instead of the FROM clause.
But this is not neccessary with your example anyway
$query = "SELECT * FROM tblmembers WHERE (emgolf = 'yes' OR emtennis = 'yes' OR emswimming = 'yes' OR emsocial = 'yes') AND (membernumber like '1%' OR membernumber like '4%' OR membernumber like '9%')";
And most sub-query queries can be re-written using joins instead.
And loose the back-ticks around your table and column names, makes me shudder. They are only needed when you are using non-standard names, and you should never use reserved words or non-standard names so you should never need the back-ticks.