## Introduction to logical operations in R

**By:** Emiley J Printer Friendly Format

Introduction to logical operations in R

There are two logical values in R, also called boolean values. They are TRUE and FALSE. In R you can construct logical expressions which will evaluate to either TRUE or FALSE.

Creating logical expressions requires logical operators. You're probably familiar with arithmetic operators like `+`, `-`, `*`, and `/`. The first logical operator we are going to discuss is the equality operator, represented by two equals signs `==`. Use the equality operator below to find out if TRUE is equal to TRUE.

`> TRUE == TRUE`

Just like arithmetic, logical expressions can be grouped by parenthesis so that the entire expression (TRUE == TRUE) == TRUE evaluates to TRUE.

To test out this property, try evaluating (FALSE == TRUE) == FALSE .

`> (FALSE == TRUE) == FALSE`

The equality operator can also be used to compare numbers. Use `==` to see if 6 is equal to 7.

`> 6 == 7`

The previous expression evaluates to FALSE because 6 is less than 7. Thankfully, there are inequality operators | that allow us to test if a value is less than or greater than another value.

The less than operator `<` tests whether the number on the left side of the operator (called the left operand) is less than the number on the right side of the operator (called the right operand). Write an expression to test whether 6 is less than 7.

`> 6 < 7`

There is also a less-than-or-equal-to operator `<=` which tests whether the left operand is less than or equal to the right operand. Write an expression to test whether 10 is less than or equal to 10.

`> 10 <= 10`

Keep in mind that there are the corresponding greater than `>` and greater-than-or-equal-to `>=` operators.

`1: 9 >= 10`

2: 6 < 8

3: 7 == 7

4: 0 > -36

2: 57 < 8

3: -6 > -7

4: 7 == 9

The next operator we will discuss is the 'not equals' operator represented by `!=`. Not equals tests whether two values are unequal, so TRUE != FALSE evaluates to TRUE. Like the equality operator, `!=` can also be used with numbers. Try writing an expression to see if 5 is not equal to 7.

`> 5 != 7`

In order to negate boolean expressions you can use the NOT operator. An exclamation point `!` will cause !TRUE (say: not true) to evaluate to FALSE and !FALSE (say: not false) to evaluate to TRUE. Try using the NOT operator and the equals operator to find the opposite of whether 5 is equal to 7.

`> !(5 == 7)`

Let's take a moment to review. The equals operator `==` tests whether two boolean values or numbers are equal, the not equals operator `!=` tests whether two boolean values or numbers are unequal, and the NOT operator `!` negates logical expressions so that TRUE expressions become FALSE and FALSE expressions become TRUE.

`1: !(0 >= -1)`

2: !FALSE

3: 7 != 8

4: 9 < 10

(TRUE != FALSE) == !(6 == 7)

At some point you may need to examine relationships between multiple logical expressions. This is where the AND operator and the OR operator come in.

Let's look at how the AND operator works. There are two AND operators in R, `&` and `&&`. Both operators work similarly, if the right and left operands of AND are both TRUE the entire expression is TRUE, otherwise it is FALSE. For example, TRUE & TRUE evaluates to TRUE. Try typing FALSE & FALSE to how it is evaluated.

`> FALSE & FALSE`

You can use the `&` operator to evaluate AND across a vector. The `&&` version of AND only evaluates the first member of a vector. Let's test both for practice. Type the expression TRUE & c(TRUE, FALSE, FALSE).

`> TRUE & c(TRUE, FALSE, FALSE)`

What happens in this case is that the left operand `TRUE` is recycled across every element in the vector of the right operand. This is the equivalent statement as c(TRUE, TRUE, TRUE) & c(TRUE, FALSE, FALSE).

Now we'll type the same expression except we'll use the `&&` operator. Type the expression TRUE && c(TRUE, FALSE, FALSE).

`> TRUE && c(TRUE, FALSE, FALSE)`

[1] TRUE

In this case, the left operand is only evaluated with the first member of the right operand (the vector). The rest of the elements in the vector aren't evaluated at all in this expression.

The OR operator follows a similar set of rules. The `|` version of OR evaluates OR across an entire vector, while the `||` version of OR only evaluates the first member of a vector.

An expression using the OR operator will evaluate to TRUE if the left operand or the right operand is TRUE. If both are TRUE, the expression will evaluate to TRUE, however if neither are TRUE, then the expression will be FALSE.

Let's test out the vectorized version of the OR operator. Type the expression TRUE | c(TRUE, FALSE, FALSE).

`> TRUE | c(TRUE, FALSE, FALSE)`

[1] TRUE TRUE TRUE

Now let's try out the non-vectorized version of the OR operator. Type the expression TRUE || c(TRUE, FALSE, FALSE).

`> TRUE || c(TRUE, FALSE, FALSE)`

[1] TRUE

Logical operators can be chained together just like arithmetic operators. The expressions: `6 != 10 && FALSE && 1 >= 2` or `TRUE || 5 < 9.3 || FALSE` are perfectly normal to see.

As you may recall, arithmetic has an order of operations and so do logical expressions. All AND operators are evaluated before OR operators. Let's look at an example of an ambiguous case. Type: 5 > 8 || 6 != 8 && 4 > 3.9

`> 5 > 8 || 6 != 8 && 4 > 3.9`

Let's walk through the order of operations in the above case. First the left and right operands of the AND operator are evaluated. 6 is not equal 8, 4 is greater than 3.9, therefore both operands are TRUE so the resulting expression `TRUE && TRUE` evaluates to TRUE. Then the left operand of the OR operator is evaluated: 5 is not greater than 8 so the entire expression is reduced to FALSE || TRUE. Since the right operand of this expression is TRUE the entire expression evaluates to TRUE.

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