Is there a way to have a function similar to else in google sheets

I have been trying to find a way for this nestled IF statement to try and work but when I try to use it, it comes up as false. I think its probably because the machine believes it has already answered the question so it doesn't run the rest of the IF statements, I'm not too sure how to fix this problem.

The letters A, B and C are the used in response to the number typed in, A will be used if the numbers 1-4 appear, B will appear if the numbers 5-8, C will appear with numbers 9-10.

=IF(C1<= 4,"A",(C1>=5<8,"B",IF(C1>=9<=10,"C")))