How to get results in IF statement

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Hello,

I have a row with cells with different numbers and under it there is another row that takes sub-sums (=B2+A3). I'd like to make an IF formula under this row to say that
IF 1.0<B2<2.0 write A or leave the cell blank
IF 3.0<B2<4.0 write B or leave the cell blank
IF 6.0<B2<7.0 write C or leave the cell blank
IF 8.0<B2<9.0 write D or leave the cell blank
I don't need more than 4 different results. I tried the IF AND but I can make only one result, (first line) I cannot make it work with all these 4 different results.

Any ideas?

Thats what I'm using so far but doesn't work
=IF(AND(B2>1,B2<2),"A",IF(AND(B2>3,B2<4),"B",IF(AND(B2>6,B2<7),"C",IF(AND(B2>8,B2<9),"D"," "))