# 3.4. Booleans¶

We’ve seen <condition> in two patterns so far: the conditional (if statements) and the while loop. Until now, we’ve just said that it should be an expression that evaluates to True or False without going into much detail. It turns out that there is a specific data type that is used for these values (True and False) and for the expressions used in conditions: the Boolean data type.

True and False are the only two values that this bool data type can have. Note that they are not strings; they aren’t written in quotation marks.

## 3.4.1. Comparison Operators¶

So if every condition for an if or while statement needs to evaluate to a Boolean value, how do we write expressions that produce the correct type? We’ve already seen some examples:

x < y
n > 0
choice == 'a'


These are Boolean expressions, meaning they each evaluate to a Boolean value. Each of those expressions is an operator with two operands. The == operator compares two operands and produces True if their values are equal and False otherwise:

>>> 5 == 5
True
>>> 5 == 6
False
>>> x = 'hello'
>>> y = 'hello'
>>> x == y
True


The complete list of comparison operators:

Operator

Interpretation

x == y

x is equal to y

x != y

x is not equal to y

x > y

x is greater than y

x < y

x is less than y

x >= y

x is greater than or equal to y

x <= y

x is less than or equal to y

Caution

Although these operations are probably familiar to you, the Python symbols are different from the mathematical symbols for the same operations. A common error is to use a single equal sign (=) instead of a double equal sign (==). But = is an assignment operator and == is a comparison operator.

Remember: = is setting something equal to a value, while == is asking a question about whether two things are equal.

Also, there is no such thing in Python as =< or =>. They’re always written like they’re most commonly said aloud: e.g., <= is “less than or equal to.”

## 3.4.2. Logical Operators¶

Sometimes we need a condition to depend on more than one comparion. For example, what if we wanted a while loop to continue as long as one variable was greater than 5 and another was less than 5? In Python, we can often (though certainly not always!) write a condition just as we would say it in English:

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 less than 10.

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 3.

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.

Caution

One common mistake for beginning programmers is to write conditions like this:

x > 0 and < 10


or like this:

age == 18 or 19 or 20


You might want to read the first example as “x is greater than 0 and less than 10,” and the second looks like “age is 18, 19, or 20.” But in Python, these are both invalid syntax! Remember that and and or are operators that take two independent Boolean operands, one on each side. That is, each side of an and or an or must be something that evaluates to True or False by itself.

On the left side of the and, x > 0 is a valid Boolean expression that will evaluate to True or False, but on the right side, < 10 is not a valid expression!

Q-1: Which of the following expressions is a correct, valid Python expression for checking whether the year variable’s value is between 1900 and 2000?

• year > 1900 < 2000
• This is invalid syntax. The '<' operator has to be given two numbers, but its left hand side in this case is a Boolean value.
• year > 1900 and < 2000
• This is invalid syntax. The 'and' operator has to be given two Boolean values, but its right hand side in this case is an invalid expression, because the '<' needs a number on its left hand side.
• year > 1900 or < 2000
• This is invalid syntax. The 'or' operator has to be given two Boolean values, but its right hand side in this case is an invalid expression, because the '<' needs a number on its left hand side.
• year > 1900 and year < 2000
• Correct!
• year > 1900 or year < 2000
• This expression will evaluate to 'True' if 'year' is holding any number at all. The 'or' evaluates to 'True' if either side is 'True', and in thise case, at least one of the two sides will always be 'True'.

Logical operators often provide a way to simplify nested conditional statements. For example, we can rewrite the following code using a single conditional:

The print statement is executed only if we make it past both conditionals, so we can get the same effect with the and operator:

if year == 1969:

You can test your code and practice writing input() statements by adding code that asks you to input a year, month, and day before the if statement.