Logical Operators

Logical Operators are essential to efficiently work with R. It is a good idea to spent some time with them and think about their possibilities and usage.

But first: What are logical operators? They are used to compare two values. The most intuitive ones are the < and > operators, for less than and larger than respectively.

4 < 5

[1] TRUE

6 > 2

[1] TRUE

As you see, both statements return the value TRUE because, — well — 4 is smaller than 5 and 6 is larger than 2. You can think of these operators as functions that takes two inputs.

Figure 1: The logical operator is a function with two arguments.

As you might guess, if there is TRUE there should also be a FALSE:

24 > 50

[1] FALSE

Logical operators will always return TRUE or FALSE, so the statements you make with them are always questions which you can answer as TRUE or FALSE. As a data type, this is called a logical (or sometimes boolean after the British mathematician George Boole).

bool <- 24 < 50
class(bool)

[1] "logical"

Overview of common logical operators

Here is a list of the most common logical operators. Again, all of these ask different questions about the relationship between two inputs. Below are a few examples.

==	equal
!=	not equal
<	less than
<=	less than or equal
>	greater than
>=	greater than or equal
%in%	is in the set

To ask the question if two values are the same we use the operator ==. Be careful to not confuse this with the assignment operator =.

1.9999999 == 2

[1] FALSE

a = 5 # one '=' means assignment
a == 5 # two '==' is the logical operator for "is equal"

[1] TRUE

One operator I find particularly useful is %in% which asks whether a value exists in a larger list of values. Reversing that question you could also say “Does my list of values contain a certain value?”

5 %in% c(1,6,4,8,6,2,5,4,9,9)

[1] TRUE

caribbean_islands = c("Cuba", "Jamaica", "Hispaniola", "Puerto Rico", "Cayman Islands")
"Sylt" %in% caribbean_islands

[1] FALSE

Logical operators and vectors

Logical operators are vectorized. This means that when we ask the question “Is the vector larger than 10?”, we get as many TRUE and FALSE answers as there are elements in the vector.

R vector logical operation

vec = c(23, 1, 60, 21, 21, 5)
vec > 10

[1]  TRUE FALSE  TRUE  TRUE  TRUE FALSE

If we safe these answers in the a new variable, we can use the result to subset the vector. So the questions “Is the vector larger than 10?” serves as an important step to do the operation “Give me all the numbers of this vector that are larger than 10!”.

large = vec > 10
vec[large]

[1] 23 60 21 21

# in short, we combine both steps to
vec[vec > 10]

[1] 23 60 21 21

There are also functions that test for certain conditions, for example if a value is of a particular class. Particularly common is the is.na() function to check for missing values.

is.numeric(5)

[1] TRUE

is.logical(5)

[1] FALSE

vec = c(1, 8, 8, NA, 6, NA, 7)

# vectorized
is.na(vec)

[1] FALSE FALSE FALSE  TRUE FALSE  TRUE FALSE

# simple check if vector contains any NA value
anyNA(vec)

[1] TRUE

How can we get rid of the NA values in this vector?

Linking logical statements

If you want to test multiple statements at once, you’ll need the following operators. This can be quit challenging for beginners. Take it step by step as in the example below.

|	or
&	and
!	not

vec = c(1, 8, 8, 6, 7)

(vec > 5) & (vec < 8)

[1] FALSE FALSE FALSE  TRUE  TRUE

Figure 2: The AND operator.

Execute the following statements and try to understand the output of each logical operator.

!anyNA(vec) & max(vec) > 5

[1] TRUE