"Hi, Amigo. Let me tell you about a new data type. The boolean. Variables of this type can take only two values: true and false."
"How do we use it?"
"This type is implicitly used in many places. Just as any addition operation produces a number, the result of any comparison is a boolean. Here are some examples:"
Code  Explanation  

1 

These two expressions are equivalent. The default value of a boolean variable is false. 
2 


3 

The result of the comparison (either true or false) will be assigned to the variable m . The condition is satisfied if the expression evaluates to true. 
4 


5 

There is no need to compare a logical (boolean) variable with true or false. The result of the comparison will be a boolean that matches the other variable. For example, true == true evaluates to true; true == false evaluates to false. 
6 

"More examples:"
Code  Explanation  

1 

This method verifies that number a is less than number b.
Here are four equivalent comparisons. The last one is the most compact and correct. Always try to use compact notation. 
2 


3 


4 

"What if I want to write 0<a<b?"
"Java doesn't have a comparison operator that takes three operands. So, you would need to do it like this: (0<a) AND (a<b)."
"Do I write the word AND?"
"Wait. I'll explain that. Java has three logical operators: AND, OR and NOT. You can use them to construct conditions of varying complexity. You can use these operators only with boolean expressions. So, you can't write (a+1) AND (3), but (a>1)AND (a<3) is OK."
"The NOT operator is unary: it affects only the expression to the right. It's more like a minus sign before a negative number rather than a multiplication sign between two numbers."
"You can perform various operations on boolean (logical) variables."
"Like what?"
"Let's take a look:"
Logical operator  Java notation  Expression  Result 

AND  &&  true && true  true 
true && false  false  
false && true  false  
false && false  false  
OR    true  true  true 
true  false  true  
false  true  true  
false  false  false  
NOT  !  ! true  false 
! false  true  
Common combinations and expressions  m && !m  false  
m  !m  true  
! (a && b)  !a  !b  
! (a  b)  !a && !b 
"Could you give me more examples?"
"Sure:"
Java notation  Logical notation 

(a<3) && (a>0)  (a < 3) AND (a>0) 
(a>10)  (a<100)  (a>10) OR (a<100) 
(a<b) && (!(c<=d))  (a<b) AND (NOT (c<=d)) 
"Now, do some tasks."
eventhen...