AN ACR FLC FLYING B737 FROM SEA RECEIVED A TCASII RA AFTER TKOF FROM AN ACFT DEPARTING A PARALLEL RWY.

Narrative

TWR CLRED US INTO POS AND HOLD ON RWY 34R AT INTXN QUEBEC. MY LAST MEMORY OF SUBSEQUENT CONFLICTING ACFT (BRASILIA) WAS ITS HOLDING SHORT OF RWY 34L FOR LNDG TFC. MY ATTN PRIOR TO POS AND HOLD CLRNC FROM TWR WAS REMINDING FO TO REPROGRAM FMC FOR RWY 34R AT QUEBEC INTXN (AS WE HAD ANTICIPATED AND INPUT AT GATE A DEP ON RWY 34L); MONITORING HIS CORRECT INPUT; CALLING FOR TKOF CHKLIST 'BELOW THE LINE' WHILE TAXIING INTO POS AFTER HAVING RECEIVED CLRNC TO DO SO. WHILE TAXIING INTO POS AND HOLD TWR CLRED US FOR TKOF -- 'NO DELAY; PLEASE; LNDG TFC ON A 2 1/2 MI FINAL' -- WE COMPLETED THE CHKLIST AND BEGAN THE TKOF ROLL. TKOF ROLL AND ROTATION WAS NORMAL; AS WAS CLBOUT TO INITIAL FLAP RETRACTION ALT; WHEN; ALL OF A SUDDEN; AN RA BEGAN COMMANDING US TO CLB. WHEN CLR OF CONFLICT FO QUERIED THE TWR AS TO THE REASON (IF KNOWN) FOR THE RA (I WAS THINKING IT WAS TFC IN THE W DOWNWIND PATTERN AT BOEING FIELD). TWR'S REMARK WAS 'THE ACFT THAT HAD JUST DEPARTED ON RWY 34L' (THE BRASILIA; ALTHOUGH WE COULDN'T SEE IT; WE THOUGHT). THIS LED US TO BEGIN THE PROCESS OF WONDERING WHETHER IN FACT WE WERE CLRED FOR TKOF AT ALL. SINCE THE TWR; WE THOUGHT; WOULD NEVER PUT US IN SUCH A POS IN THE FIRST PLACE; WOULD THEY? DEBATING THE ISSUE BACK AND FORTH BTWN US FOR THE NEXT HR WE WERE BOTH CONVINCED WE DID RECEIVE TKOF CLRNC SINCE I VERBALIZED THE CLRNC OUT LOUD (AS IS MY CUSTOMARY MANNER) AND THE FO READ BACK THE CLRNC TO THE TWR. WE DID NOT RECEIVE ANY SUBSEQUENT REQUEST FROM THE TWR; DEP; OR CTR TO CALL THEM ON REACHING DEST.