Boolean algebra is a subarea of algebra where variables can only have two values: true or false (usually 1 and 0). Instead of addition and multiplication, the main operations in Boolean algebra are conjunction (AND), disjunction (OR), and negation (NOT). Truth tables define the output of each logical operation based on the binary inputs. Boolean algebra is used to represent logical statements and relationships between variables algebraically.

1. Boolean Algebra

2. Boolean Algebra
• In mathematics and mathematical logic,
Boolean algebra is the subarea of algebra in
which the values of the variables are the truth
values true and false, usually denoted 1 and 0
respectively

3. Boolean Algebra
• Instead of elementary algebra where the
values of the variables are numbers, and the
main operations are addition and
multiplication, the main operations of Boolean
algebra are the conjunction and, denoted .,
the disjunction or, denoted +, and the
negation not, denoted ¯.

4. Truth Table
X Y X . Y X + Y
0 0 0 0
0 1 0 1
1 0 0 1
1 1 1 1
X ¯X
0 1
1 0

5. Example

6. Logical equivalence
• 0 corresponds to F (false)
• 1 corresponds to T (true).
• logical operators,
• Not - ￢
• Or- ∨
• And- ∧

7. Example
• Translate 1 ・ 0 + (0 + 1) = 0, into a logical
equivalence

8. Example

9. Example
• Find the values of the Boolean function
represented by F(x, y) = .
x y ¯y
0 0 1 0
0 1 0 0
1 0 1 1
1 1 0 0

10. Example
• Find the values of the Boolean function
represented by F(x, y, z) =

11. Example
• Translate the x + yz = (x + y)(x + z) into a logical
equivalence

14. Thank you