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Default To leave a cell blank following an "IF" function

How can I leave a cell blank following a response to an "IF" function?
Because in Excel 2007, the default response in a cell is "FALSE" when I leave
a cell in question to the "IF" function blank. This is because I would like
to be able to leave those cells in question to the function as blank or not
depending on the data that I would like to show.

Example: [in cell B1: IF(A1="a",1,IF(A1="b",2,IF(A1="c",3)))] in this
example, B1 returns "FALSE" when I leave A1 blank but I would like it to be
able to remain blank and not show "FALSE". What I was thinking is that the
function for a dropdown menu would do the job but I cannot get it to work the
way I would like it to so I am using the "IF" function instead.

What I have now is a dropdown menu in A1 (from data in another Worksheet)
and when I select a certain data from this menu, I would like Excel to
automatically put corresponding data in cells B1 and B2. And the only way I
know how it can do what I want it to do is to use the "IF" function in B1, B2
etc... but there is a bit of data in criteria to the "IF" function that this
function returns an error because there are too many functions within this
function.

Hope this makes sense.
 
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