Solving Boolean Algebra Qns: x+yz+x'y= (x+x')(x+y)+yz

Is there a specific reason for using this method?In summary, the conversation is about a question on boolean algebra and a specific part of an equation that the person does not understand. Another person suggests using absorption to replace x with x(x+y) and adds xx' because it's equal to 0, resulting in (x+x')(x+y). The person then questions the reason for using this method.
  • #1
jaydunkfull
1
0
hi all

ive got a short qns on boolean algebra. here's the qns

x+yz+x'y= (x+x')(x+y)+yz

this is just a small part of the eqn i do not understand. how does x+x'y become (x+x')(x+y)? i don't seem to be able to apply any other laws that lead to this.

thanks in advance!
 
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  • #2
You can use absorption to replace x with x(x+y) and add xx' since it's equal to 0 to get

x+x'y = x(x+y) + x'x + x'y = x(x+y) + x'(x+y) = (x+x')(x+y)

Seems kind of a roundabout way to show x+x'y = x+y.
 

FAQ: Solving Boolean Algebra Qns: x+yz+x'y= (x+x')(x+y)+yz

1. What is Boolean algebra?

Boolean algebra is a branch of mathematics that deals with operations on variables that can only have two possible values: true or false. It is used to represent logical statements and make deductions based on these statements.

2. How do I solve Boolean algebra equations?

To solve Boolean algebra equations, you need to use the basic logical operations of AND, OR, and NOT. These operations can be represented using symbols, such as "+" for OR, "." for AND, and "'" for NOT. The goal is to simplify the equation by using the properties of these operations and reduce it to its simplest form.

3. What is the purpose of using Boolean algebra?

Boolean algebra is used to simplify complex logical statements and make deductions based on these statements. It is also used in computer science and digital electronics to design and optimize logical circuits.

4. Can you explain the steps to solve the given Boolean algebra equation?

Sure, the first step is to distribute the terms within the parentheses using the distributive property. This will result in x+x'y+xy+x'y. Then, you can combine like terms, in this case, x and x'y. This will give you x+y+xy. Finally, you can use the associative and commutative properties to rearrange the terms and simplify it to x+y.

5. What are some common mistakes to avoid when solving Boolean algebra equations?

Some common mistakes to avoid include forgetting to use parentheses, not applying the correct order of operations, and not simplifying the equation to its simplest form. It is also important to keep track of the variables and their values throughout the solving process.

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