The IF function allows you to make a logical comparison between a value and what you expect by testing for a condition and returning a result if that condition is True or False.

=IF(Something is True, then do something, otherwise do something else)
But what if you need to test multiple conditions, where let’s say all conditions need to be True or False (AND), or only one condition needs to be True or False (OR), or if you want to check if a condition does NOT meet your criteria? All 3 functions can be used on their own, but it’s much more common to see them paired with IF functions.
Technical Details
Use the IF function along with AND, OR and NOT to perform multiple evaluations if conditions are True or False.
Syntax

IF(AND())  IF(AND(logical1, [logical2], ...), value_if_true, [value_if_false]))

IF(OR())  IF(OR(logical1, [logical2], ...), value_if_true, [value_if_false]))

IF(NOT())  IF(NOT(logical1), value_if_true, [value_if_false]))
Argument name 
Description 

logical_test (required) 
The condition you want to test. 

value_if_true (required) 
The value that you want returned if the result of logical_test is TRUE. 

value_if_false (optional) 
The value that you want returned if the result of logical_test is FALSE. 

Here are overviews of how to structure AND, OR and NOT functions individually. When you combine each one of them with an IF statement, they read like this:

AND – =IF(AND(Something is True, Something else is True), Value if True, Value if False)

OR – =IF(OR(Something is True, Something else is True), Value if True, Value if False)

NOT – =IF(NOT(Something is True), Value if True, Value if False)
Examples
Following are examples of some common nested IF(AND()), IF(OR()) and IF(NOT()) statements. The AND and OR functions can support up to 255 individual conditions, but it’s not good practice to use more than a few because complex, nested formulas can get very difficult to build, test and maintain. The NOT function only takes one condition.
Here are the formulas spelled out according to their logic:
Formula  Description 

=IF(AND(A2>0,B2<100),TRUE, FALSE) 
IF A2 (25) is greater than 0, AND B2 (75) is less than 100, then return TRUE, otherwise return FALSE. In this case both conditions are true, so TRUE is returned. 
=IF(AND(A3="Red",B3="Green"),TRUE,FALSE) 
If A3 (“Blue”) = “Red”, AND B3 (“Green”) equals “Green” then return TRUE, otherwise return FALSE. In this case only the first condition is true, so FALSE is returned. 
=IF(OR(A4>0,B4<50),TRUE, FALSE) 
IF A4 (25) is greater than 0, OR B4 (75) is less than 50, then return TRUE, otherwise return FALSE. In this case, only the first condition is TRUE, but since OR only requires one argument to be true the formula returns TRUE. 
=IF(OR(A5="Red",B5="Green"),TRUE,FALSE) 
IF A5 (“Blue”) equals “Red”, OR B5 (“Green”) equals “Green” then return TRUE, otherwise return FALSE. In this case, the second argument is True, so the formula returns TRUE. 
=IF(NOT(A6>50),TRUE,FALSE) 
IF A6 (25) is NOT greater than 50, then return TRUE, otherwise return FALSE. In this case 25 is not greater than 50, so the formula returns TRUE. 
=IF(NOT(A7="Red"),TRUE,FALSE) 
IF A7 (“Blue”) is NOT equal to “Red”, then return TRUE, otherwise return FALSE. 
Note that all of the examples have a closing parenthesis after their respective conditions are entered. The remaining True/False arguments are then left as part of the outer IF statement. You can also substitute Text or Numeric values for the TRUE/FALSE values to be returned in the examples.
Here are some examples of using AND, OR and NOT to evaluate dates.
Here are the formulas spelled out according to their logic:
Formula  Description 

=IF(A2>B2,TRUE,FALSE) 
IF A2 is greater than B2, return TRUE, otherwise return FALSE. 03/12/14 is greater than 01/01/14, so the formula returns TRUE. 
=IF(AND(A3>B2,A3<C2),TRUE,FALSE) 
IF A3 is greater than B2 AND A3 is less than C2, return TRUE, otherwise return FALSE. In this case both arguments are true, so the formula returns TRUE. 
=IF(OR(A4>B2,A4<B2+60),TRUE,FALSE) 
IF A4 is greater than B2 OR A4 is less than B2 + 60, return TRUE, otherwise return FALSE. In this case the first argument is true, but the second is false. Since OR only needs one of the arguments to be true, the formula returns TRUE. If you use the Evaluate Formula Wizard from the Formula tab you'll see how Excel evaluates the formula. 
=IF(NOT(A5>B2),TRUE,FALSE) 
IF A5 is not greater than B2, then return TRUE, otherwise return FALSE. In this case, A5 is greater than B2, so the formula returns FALSE. 
Using AND, OR and NOT with Conditional Formatting
You can also use AND, OR and NOT to set Conditional Formatting criteria with the formula option. When you do this you can omit the IF function and use AND, OR and NOT on their own.
From the Home tab, click Conditional Formatting > New Rule. Next, select the “Use a formula to determine which cells to format” option, enter your formula and apply the format of your choice.
Using the earlier Dates example, here is what the formulas would be.
Formula  Description 

=A2>B2 
If A2 is greater than B2, format the cell, otherwise do nothing. 
=AND(A3>B2,A3<C2) 
If A3 is greater than B2 AND A3 is less than C2, format the cell, otherwise do nothing. 
=OR(A4>B2,A4<B2+60) 
If A4 is greater than B2 OR A4 is less than B2 plus 60 (days), then format the cell, otherwise do nothing. 
=NOT(A5>B2) 
If A5 is NOT greater than B2, format the cell, otherwise do nothing. In this case A5 is greater than B2, so the result will return FALSE. If you were to change the formula to =NOT(B2>A5) it would return TRUE and the cell would be formatted. 
Note: A common error is to enter your formula into Conditional Formatting without the equals sign (=). If you do this you’ll see that the Conditional Formatting dialog will add the equals sign and quotes to the formula  ="OR(A4>B2,A4<B2+60)", so you’ll need to remove the quotes before the formula will respond properly.
Need more help?
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See Also
See a video on how to use the IF function
Learn how to use nested functions in a formula