Boolean Algebra- having trouble solving

In summary, the conversation is about a simplified equation AB + (A' + B')C + AB and the attempt at solving it. The solution is AB + C, which can be reached by working backwards and using DeMorgan's theorem.
  • #1
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0

Homework Statement



AB + (A' + B')C + AB


Homework Equations



I've simplified many problems, but this one is giving me trouble. I know the answer is AB + C, but for some mental reason, I can't seem to come to that answer.

The Attempt at a Solution



STEP 1: AB + A'C + B'C + AB
STEP 2: AB + A'C + B'C <-- AB + AB = AB
STEP 3: not sure where to go from here...

ANSWER= AB + C


Thanks for any help :)
 
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  • #2
If
AB + A'C + B'C

Then
AB + A'BC + AB'C + A'B'C

Then
AB + C(A'B + AB' + A'B')

It should be obvious that AB + A'B + AB' + A'B' = 1 but how to reduce down to AB + C, I don't know.
 
  • #3
Ok, I figured out the answer... you need to work backwards, as follows;



Original Equation --- > AB + (A' + B')C + AB

STEP 1: AB + (A' + B')C + AB
STEP 2: AB + (A' + B')C <--- AB+AB=AB, so one AB is removed
STEP 3: AB + (AB)'C <--- On this step you took a step backwards
Step 4: AB+C <--- Now, according to demorgans theorem, 11, you ca cancel the AB'

Answer AB+C

Tough one...
 

1. What is Boolean Algebra?

Boolean Algebra is a branch of mathematics that deals with logical statements and operations. It is used to analyze and simplify logical expressions, which are commonly used in computer programming and digital electronics.

2. What are the basic operations in Boolean Algebra?

The basic operations in Boolean Algebra are AND, OR, and NOT. These operations are used to combine and manipulate logical statements to produce new statements.

3. How do I represent Boolean expressions?

Boolean expressions can be represented using variables and logical operators. Variables can have two possible values: true (represented by 1) or false (represented by 0). Logical operators, such as AND, OR, and NOT, are used to connect these variables and create logical statements.

4. How do I simplify a Boolean expression?

To simplify a Boolean expression, you can use Boolean laws and theorems, such as the distributive law, De Morgan's laws, and the identity laws. These laws and theorems allow you to manipulate the expression and reduce it to its simplest form.

5. How is Boolean Algebra used in real-life applications?

Boolean Algebra is widely used in computer programming, digital electronics, and circuit design. It is also used in database systems and search algorithms. Additionally, many everyday devices, such as computers and smartphones, use Boolean Algebra in their operations.

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