6.3. Logical operators

There are three logical operators: and, or, and not. All three operators take boolean operands and produce boolean values. The semantics (meaning) of these operators is similar to their meaning in English:

Look at the following example. See if you can predict the output. Then, run it to see if your predictions were correct:

Although you can use boolean operators with simple boolean literals or variables as in the above example, they are often combined with the comparison operators, as in this example. Again, before you run this, see if you can predict the outcome:

The expression x > 0 and x < 10 is True only if x is greater than 0 and at the same time, x is less than 10. In other words, this expression is True if x is between 0 and 10, not including the endpoints.

Common Mistake!

There is a very common mistake that occurs when programmers try to write boolean expressions. For example, what if we have a variable number and we want to check to see if its value is 5 or 6. In words we might say: “number equal to 5 or 6”. However, if we translate this into Python, number == 5 or 6, it will not yield correct results. The or operator must have a complete equality check on both sides. The correct way to write this is number == 5 or number == 6. Remember that both operands of or must be booleans in order to yield proper results.

The or operator is sometimes confusing to new programmers, because it operates differently than the way we use the word ‘or’ when speaking. The sentence, ‘’Karina is going to go to grad school or look for a job in industry’’ suggests that Karina will do one of these two things, but will not do both. In English, the ‘or’ we typically use is what we call an ‘exclusive or’. But in programming, the value of an or expression is true if both operands are true. The only time an or expression evaluates to false is when both operands are false. In the Karina example, it would be true if Karina went to grad school, it would be true if Karina got a job in industry, it would be true if Karina went to grad school and got a job in industry. It would only be false if Karina did neither.

6.3.1. Smart Evaluation

Python is “smart” about the way it evaluates expressions using boolean operators. Consider the following example:

answer = input('Continue?')
if answer == 'Y' or answer == 'y':

There are two operands for the or operator here: answer == 'Y' and 'answer == 'y'. Python evaluates from left to right, and if the first operand for or evaluates to True, Python doesn’t bother evaluating the second operand, because it knows the result must be True (recall that if either operand for or is True, the result is True). So, if the user enters Y, Python first evaluates answer == 'Y', determines that it is True, and doesn’t bother to check to see if answer == 'y' is True; it just concludes that the entire condition is True and executes the print statement.

In a similar fashion, with the and operator, if the first operand evaluates to False, Python doesn’t check the second operand’s value, because it can conclude that the result must be False.

This behavior, in which Python in some cases skips the evaluation of the second operand to and and or, is called short-circuit boolean evaluation. You don’t have to do anything to make Python do this; it’s the way Python works. It saves a little processing time. And, as a special bonus, you can take advantage of Python’s short-circuiting behavior to shorten your code. Consider the following example:

This code checks to see if the average weight of a given number of pieces of luggage is greater than 50 pounds. However, there is a potential crash situation here. If the user enters 0 for num_pieces, the program will crash with a divide by zero error. Try it out to see it happen.

To prevent the crash, you might add an extra if statement to check for zero:

if num_pieces != 0:
   if total_weight / num_pieces > 50:
      print('Average weight is greater than 50 pounds -> $100 surcharge.')

Now, the division will not occur if num_pieces is zero, and a potential runtime crash has been averted. Good job!

We can shorten this example to a single if statement if we do it carefully. Anytime you have two nested if statements as in the example above, you can combine them into a single if statement by joining the conditions using the and operator. Consider the version below, and think about why this if statement is equivalent in its behavior to the previous version with two nested if statements:

But wait a minute: is this code safe? Try running the program and entering the value 500 for total_weight and the value 5 for num_pieces. Then, try it again using the value 0 for num_pieces. There should be no crash.

Next, try altering the code and reversing the order of the if conditions:

if total_weight / num_pieces > 50 and num_pieces != 0:
   print('Average weight is greater than 50 pounds -> $100 surcharge.')

Run the program again, performing the same two tests. This time, you should observe a crash when you enter 0 for num_pieces. Can you analyze why the first version did not crash, but the second one does?

In the second version, when evaluating left-to-right, the division by zero occurs before Python evaluates the comparison num_pieces != 0. When joining two if statements into a single if statement, you must be sure to put the condition from the first if statement on the left-hand side of the and operator, and the other condition on the right-hand side, in order to get the same effect.

To summarize this discussion on smart evaluation, keep in mind that when you are performing potentially dangerous operations in an if statement or while loop using boolean logic with and or or, order matters!

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