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Default what is syntax for if(between range of dates,"Q1","Q2")?

HI,
I'm trying to create the following formula:

if cell b34 is between Nov 1/04 and Jan 31/05, enter "Q1"
if cell b34 is between Feb 1/05 and April 30/05, enter "Q2"

etc.
What is the correct syntax for this formula? I have entered:

if(11/01/04<=b34<=01/31/05,"Q1",if(02/01/05<=b34<=04/30/05,"Q2",if(etc etc)))

But this isn't working.

Does anyone know how to create an If statement based on a cell falling
within a range of dates?