Logical Expressions

When we learned about data types, we promised that we would talk about boolean values in greater depth in the future. That future is now.

So far, we know that the boolean data type has two values, True and False. We also know that underneath it all, our computers are executing machine code to manipulate binary data (“bits”) that are 1s and 0s. The boolean data type maps directly to these 1s (True/”on”) and 0s (False/”off”).

Take a look at what happens when we cast boolean values to ints.

# TODO: run this code
int(True)

# TODO: run this code
int(False)

Logical expressions are what we call all expressions that evaluate to either True or False. These expressions may involve one or both of comparison operators and logical operators.

Comparison Operators

Comparison operators compare two values (any type) and give back the result of True or False. Some of these comparison operators you may have seen previously in math classes, but some you probably haven’t.

value1 < value2  # less than
value1 <= value2  # less than or equal to 
# (NOTE! "=<" does NOT work!)

value1 > value2  # greater than
value1 >= value2  # greater than or equal to 
# (NOTE! "=<" does NOT work!)

value1 == value2  # equal
value1 != value2  # not equal

Before you play around with these, let’s pay special attention to the fact that to test equality, we must use ==, NOT =. This is because just = is what’s called the assignment operator. It is how we assign a value to a variable, which is very different than testing for equality!

# TODO: run this code.
# Play around with the comparison operators
# Can you use < between floats? strings? 
# what does < between strings test for?
# Answer:

1 < 3 

# TODO: investigate what happens when you 
# compare strings. What makes a string "less than"
# or "greater than" another string?
# Is capitalization important?
# Answer:

"cat" > "alpaca"

# TODO: run this code.
# Fix the SyntaxError
1.0 = 1

# TODO: run this code.
# What do you think this expression will evaluate to?
# Does it?
0.0000000000000000000001 == 0

# TODO: run this code.
# What do you think this expression will evaluate to?
# Does it?
"Flamingo" != "flamingo"

# TODO: run this code.
# What do you think this expression will evaluate to?
# Does it?
"yes" == "YeS"

Comparison operators have lower precedence than all of our mathematical operators. For example, in the expression:

3 + 4 < 5

The 3 + 4 will be evaluated before the less than comparison operator.

Comparison operators include ==,!=,<=,>=,>,<, and in.

in can be used with strings and lists to test for membership (“is there an "a" in "cat"?”). We’ll look at in in more depth when we look at lists.

Logical Operators

The second piece of the logic puzzle is the logical operator. A logical operator is similar to a comparison operator except that it only operates on boolean values. It’s job is to take either one or two boolean values and give you back one new boolean value.

Our logical operators are:

# and (two boolean values -> one boolean value)
boolean_value1 and boolean_value2  

# or (two boolean values -> one boolean value)
boolean_value1 or boolean_value2

# not (one boolean value -> one boolean value)
not boolean_value1  # not

We’ll concentrate on and and or for the time being (though we encourage you to play around with not!).

and

Think of and as translating to: True if both the first value and the second value are True.

For instance, if you wanted a value of True if someone was both at least 18 and a Colorado resident, you might have code like:

age = 19
residency = "Colorado"
print(age >= 18 and residency == "Colorado")

# TODO: play with the "and" logical operator.
# What happens if one of the values is false?
# What happens if both of the values are false?
# Answer:

or

Think of or as translating to: True if either the first value or the second value is True.

For instance, if you wanted a value of True if someone was either an INFO major or a CSCI major:

name = "Mohamed"
major = "INFO"
print(major == "INFO" or major == "CSCI")

# TODO: run this code!
name = "Mohamed"
major = "INFO"
print(major == "INFO" or major == "CSCI")

# TODO: run this code!
name = "Susan"
major = "ATOC"
print(major == "INFO" or major == "CSCI")

# TODO: run this code! What happens?
# Answer:
major = "ENGL"
major == "INFO" or "CSCI"

In the cell above we have code that doesn’t quite do what we wanted it to. We’ve put it here because this is a common bug when writing logical expressions. Even if you are testing the value of the same variable twice, you must write the name of the variable again (because python isn’t as smart as you or I, we have to be very very explicit about everything!).

See the section on not for more information on this logical expression.