Excel uses the ; sign to define where the conditions of the (for example) IF function starts and ends (same is with all other functions) since excel is kind of a simplified programming language u can think of the ; sign as a carriage return, whereas the , sign is used only to combine references or arrays of values (cells). By defining the IF function by commas you basically just told the excel the argument which you want to be tested for true or false, but you did not state what is the true and false condition result, so the probable result will be an error. check your syntax for properly set ; signs.
the IF function (also nearly any function) in excel works as it works in any programming language
IF(something you need tested for true or false) then TRUE is something FALSE is something else
in excel it works like
if a1 is larger than a2 then the cell containing the function will result in value of cell b1
else if a1 is not larger than a2 the cell will contain value of cell b2
actually is not a valid function meaning that u test if A1 is larger than the intersection of A2 B1 and B2 which is impossible by logic because A2 B1 and B2 are cells not arrays or references so they can't have intersections that is why u get an error message. and supplemental to that in the above function there is no value for TRUE or FALSE defined so that is not a complete function and therefore can't be executed
The INDEX function is basically useless by itself. not completely useless but is better when used with other functions
is is used for referencing, lets make it complex like
the cell containing the func will result in a value from the array from a1 to f10, and the result will be if h5 is larger than m5 from the second row in the array if not larger from the fourth row, and if g1 is larger than n1 from the first column and if not larger from the fifth column.
meaning the value will be the intersection of the ROW and COLUMN in the given ARRAY
again, from the ARRAY, not the actual row and column numbers
and for the $ sign, as far as I know it is used for showing US currency nothing else. i'm not familiar with any other usage of it in excel.