Logical Operators and Complex Boolean Expressions

A more complex Boolean expression can be built of simpler Boolean expressions and can be written as

Boolean_Expression1 Logical Operator Boolean_Expression2

where

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Logical Operator	Description
&&	AND (also known as logical conjunction)
\|\|	OR (also known as logical disjunction)
!	NOT (also known as negation or logical complement)

The truth table for all three operators is shown here.

Are you still confused? You shouldn’t be! It is quite simple!

The result of the logical operator AND ( && ) is true when both BE1 and BE2 are true.
The result of the logical operator OR ( || ) is true when either BE1 or BE2 is true (at least one).
The logical operator NOT ( ! ) just reverses the result of a Boolean expression. In this table, when BE1 is true the result is false and vice versa.

Notice: In flowcharts, this website uses the commonly accepted AND, OR, and NOT operators!

Next are some examples of complex Boolean expressions. The parentheses are not really necessary. They are used just for increased readability.

(x == 5) && (x > y). This can be read as “test if x is equal to 5 and greater than y”
(x > y) || (x == 3). This can be read as “test if x is greater than y or equal to 3”
!(x < y). This can be read as “test if x is not less than y” or, in other words, “test if x is greater than or equal to y”

Notice: In the last Boolean expression, please note the exclamation mark in the front.

Logical Operator	Description
And	Also known as logical conjunction
Or	Also known as logical disjunction
Not	Also known as negation or logical complement

The truth table for all three operators is shown here.

Are you still confused? You shouldn’t be! It is quite simple!

The result of the logical operator And is true when both BE1 and BE2 are true.
The result of the logical operator Or is true when either BE1 or BE2 is true (at least one).
The logical operator Not just reverses the result of a Boolean expression. In this table, when BE1 is true the result is false and vice versa.

Next are some examples of complex Boolean expressions. The parentheses are not really necessary. They are used just for increased readability.

(x = 5) And (x > y). This can be read as “test if x is equal to 5 and greater than y”
(x > y) Or (x = 3). This can be read as “test if x is greater than y or equal to 3”
Not(x < y). This can be read as “test if x is not less than y” or, in other words, “test if x is greater than or equal to y”

Logical Operator	Description
and	Also known as logical conjunction
or	Also known as logical disjunction
not	Also known as negation or logical complement

The truth table for all three operators is shown here.

Are you still confused? You shouldn’t be! It is quite simple!

The result of the logical operator and is true when both BE1 and BE2 are true.
The result of the logical operator or is true when either BE1 or BE2 is true (at least one).
The logical operator not just reverses the result of a Boolean expression. In this table, when BE1 is true the result is false and vice versa.

Next are some examples of complex Boolean expressions. The parentheses are not really necessary. They are used just for increased readability.

(x == 5) and (x > y). This can be read as “test if x is equal to 5 and greater than y”
(x > y) or (x == 3). This can be read as “test if x is greater than y or equal to 3”
not(x < y). This can be read as “test if x is not less than y” or, in other words, “test if x is greater than or equal to y”