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query MySQL should return only unbooked

I were given three tables

Lakes - identification,name,lat,lon

Pegs - id, pegnumber, pegname,lake_id

Reservations- identity, start_day,end_day , peg_id

I am attempting to write the question who return me the listing of unbooked pegs on a lake at some point or among two dates. I wrote that query however they return me best already booked.

SELECT l.name,p.id,p.peg_number,r.start_day,r.end_day     

FROM reservations r 

left join pegs  p on r.peg_id = p.id 

left join lakes l on p.lake_id = l.id

WHERE r.start_day is not null 

order by l.name