Fax: 1- 425- 458- 9358 |
Toll free: 1- 877- 252 - 7763
Forgot Password? Click Here
Register
| Account
Boolean algebra
A Boolean algebra is a logic algebra. The variables X can take on either of two values corresponding to truth (1 or T) and false (0 or F).
Not X is denoted by ∼X
If X = 1 then ∼X = 0.
If X = 0 then ∼X = 1.
A or B is denoted by A ∪ B (sometimes A + B).
A = 1 and B = 1 ⇒(implies) A ∪ B = 1.
A = 1 and B = 0 ⇒ A ∪ B = 1.
A = 0 and B = 1 ⇒ A ∪ B = 1.
A = 0 and B = 0 ⇒ A ∪ B = 0.
A and B is denoted by A ∩ B (sometimes A B).
A = 1 and B = 1 ⇒ A ∩ B = 1.
A = 1 and B = 0 ⇒ A ∩ B = 0.
A = 0 and B = 1 ⇒ A ∩ B = 0.
A = 0 and B = 0 ⇒ A ∩ B = 0.
The laws of logic:
Associativity:
(A ∪ B) ∪ C = A ∪ (B ∪ C)
(A ∩ B) ∩ C = A ∩ (B ∩ C)
Commutivity:
A ∪ B = B ∪ A
A ∩ B = B ∩ A
Negation:
∼ 1 = 0
∼ 0 = 1
Double negation:
∼∼ X = X
Distributive property:
A ∪ (B ∩ C ) = (A ∪ B) ∩ (A ∪ C)
A ∩ (B ∪ C ) = (A ∩ B) ∪ (A ∩ C)
Complementary property:
A U ( ∼ A ) = 1
A ∩ ( ∼ A ) = 0
Absorption property:
A U A = A
A ∩ A = A
A U 1 = 1
A ∩ 0 = 0
Identity property:
A ∩ 1= A
A U 0 = A
DeMorgan’s Laws:
∼ (A ∩ B) = ( ∼ A ) U ( ∼ B )
∼ (A U B) = ( ∼ A ) ∩ ( ∼ B )
Logic operator:
A = 1 and B = 1 ⇒ A U B =1
A = 1 and B = 0 ⇒ A U B =1
A = 0 and B = 1 ⇒ A U B =1
A = 0 and B = 0 ⇒ A U B =0
Truth table:
A or B
| 1 | 0 | |
| 1 | 1 | 1 |
| 0 | 1 | 0 |
Not A
| 1 | |
| 1 | 0 |
| 0 | 1 |
A and B
| 1 | 0 | |
| 1 | 1 | 0 |
| 0 | 0 | 0 |
Other logical relations are equivalence and implies.
A EQUI B
| 1 | 0 | |
| 1 | 1 | 0 |
| 0 | 0 | 1 |
A IMPLIES B
| 1 | 0 | |
| 1 | 1 | 0 |
| 0 | 1 | 1 |
| Name* : |
|||||
| Email* : |
|||||
| Country* : |
|||||
| Phone* : |
|||||
| Subject* : |
|||||
| Upload Homework : Upload another homework (upto 5 uploads max.)
|
|||||
| Due Date |
Time |
AM/PM |
Timezone |
||
| Instructions |
|||||
|
|||||
| Courses/Topics we help on | ||
| Discrete Mathematics | Applied Calculus I | Applied Calculus II |
| Healthcare Statistics and Research | Advanced Engineering Mathematics I |
Advanced Engineering Mathematics II |
| Introduction to Algebra | Basic Algebra | Algebra for College Students |
| Algebra for College Students | Pre-Calculus | Statistics for Decision-Making |
| Polar Co-ordinates | Area in Polar Coordinates | Solving Systems of Equations |
| Systems of Inequalities | Quadratic Equations | Matrices and System of Equations |
| The Determinant of a Square Matrix | Cramer's Rule | Ellipse |
| Hyperbola | Rate of Change | Measurement of Speed |
| Finding Limits Graphically | Higher Order Derivatives | Rolle's Theorem and Mean Value Theorem |
| Concavity and Second Derivative Test | Limits at Infinity | Indefinite Integration |
| Definite Integration | Integration by Substitution | Area of a Region Between Two Curves |
| Volume by Shell Method and Disc Method | Integration by Parts | Trigonometric Integration |
| Differential Equations | Slope Fields | Growth and Decay |
| System of Differential Equations | Parametric Equations | Complex Numbers |
| The Inverse of a Square Matrix | Parabola | Functions and Their Graphs |
| Evaluating Limits Analytically | Increasing and Decreasing Functions | Newton's Method |
| Finding Area Using Integration | Numerical Integration | Moments |
| Partial Fractions | Separation of Variables | Second Order Differential Equations |
| IB Maths | ||
