7.2. Logical operators

There are three logical operators: and, or, and not. The semantics (meaning) of these operators is similar to their meaning in English. For example, x > 0 and x < 10 is true only if x is greater than 0 and at the same time, x is less than 10. How would you describe this in words? You would say that x is between 0 and 10, not including the endpoints.

n % 2 == 0 or n % 3 == 0 is true if either of the conditions is true, that is, if the number is divisible by 2 or divisible by 3. In this case, one, or the other, or both of the parts has to be true for the result to be true.

Finally, the not operator negates a boolean expression, so not  x > y is true if x > y is false, that is, if x is less than or equal to y.

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 5,6, or 7. In words we might say: “number equal to 5 or 6 or 7”. However, if we translate this into Python, number == 5 or 6 or 7, it will not be correct. The or operator must join the results of three equality checks. The correct way to write this is number == 5 or number == 6 or number == 7. This may seem like a lot of typing but it is absolutely necessary. You cannot take a shortcut.

Check your understanding

    select-2-1: What is a correct Python expression for checking to see if a number stored in a variable x is between 0 and 5?

  • x > 0 and < 5
  • Each comparison must be between exactly two values. In this case the right-hand expression < 5 lacks a value on its left.
  • x > 0 or x < 5
  • Although this is legal Python syntax, the expression is incorrect. It will evaluate to true for all numbers that are either greater than 0 or less than 5. Because all numbers are either greater than 0 or less than 5, this expression will always be True.
  • x > 0 and x < 5
  • Yes, with an and keyword both expressions must be true so the number must be greater than 0 an less than 5 for this expression to be true. Although most other programming languages do not allow this mathematical syntax, in Python, you could also write 0 < x < 5.
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