Solve Boolean Identities: xy+x’z+yz’=xy+x’z

  • Thread starter syedejaz
  • Start date
In summary: Dear I am very sorry.Our university corrected the mistake . They published it on the web.here is the correctxy+x’z+yz=xy+x’z ThanksIn summary, the conversation is about a user seeking help in solving a question involving Boolean algebra identities. The problem is originally stated as xy+x’z+yz’=xy+x’z, but after realizing a mistake, the correct equation is given as xy+x’z+yz=xy+x’z. The user is looking for guidance in using the basic identities of Boolean algebra to show that the two sides of the equation are equal.
  • #1
syedejaz
5
0
Dear all please help me in solving this question:
I tried my best but I was not able to solve.

Using the basic identities of Boolean algebra show that :
xy+x’z+yz’=xy+x’z


Kindly help me.
 
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  • #2
syedejaz said:
Dear all please help me in solving this question:
I tried my best but I was not able to solve.

Using the basic identities of Boolean algebra show that :
xy+x’z+yz’=xy+x’z


Kindly help me.

Welcome to the PF.

What are the basic Boolean identity equations? Please list them for us, and tell us which ones you think might apply.
 
  • #3
berkeman said:
Welcome to the PF.

What are the basic Boolean identity equations? Please list them for us, and tell us which ones you think might apply.

Thank you so much
here is the table from my course book
Untitled-1-2.jpg
 
Last edited:
  • #4
BTW, are you sure you copied the equation down correctly?

xy+x’z+yz’=xy+x’z


The lefthand side (LHS) and righthand side (RHS) are the same, except for one extra term on the LHS...
 
  • #5
berkeman said:
BTW, are you sure you copied the equation down correctly?

xy+x’z+yz’=xy+x’z


The lefthand side (LHS) and righthand side (RHS) are the same, except for one extra term on the LHS...

And if you check this with two Karnaugh maps (one for LHS and one for RHS), they differ...
 
  • #6
berkeman said:
BTW, are you sure you copied the equation down correctly?

xy+x’z+yz’=xy+x’z


The lefthand side (LHS) and righthand side (RHS) are the same, except for one extra term on the LHS...

yes offcourse
 
  • #7
hello no body knows ): please help me I have to submit my Assigment tomorrow.
 
  • #8
syedejaz said:
yes offcourse

What do you mean "of course"? The LHS does not equal the RHS, so how can you use any manipulations to show that they are equal?
 
  • #9
berkeman said:
What do you mean "of course"? The LHS does not equal the RHS, so how can you use any manipulations to show that they are equal?

Dear I am very sorry.
Our university corrected the mistake . They published it on the web.
here is the correct

xy+x’z+yz=xy+x’z

Thanks
 

FAQ: Solve Boolean Identities: xy+x’z+yz’=xy+x’z

What is a Boolean identity?

A Boolean identity is an equation or statement that is always true for any values of the variables involved. In other words, it is a mathematical expression that follows the laws and rules of Boolean algebra.

How do you solve a Boolean identity?

To solve a Boolean identity, you need to use the laws and rules of Boolean algebra to manipulate the expression until it is simplified and matches the original equation. This often involves using properties such as the distributive, associative, and commutative properties.

What are the steps to solve xy+x’z+yz’=xy+x’z?

The steps to solve this Boolean identity are as follows:

  1. Use the distributive property to expand the expression.
  2. Combine like terms (terms with the same variables and exponents).
  3. Apply the associative and commutative properties to rearrange the terms.
  4. Use the identity property to cancel out any terms that are equal to 0 or 1.
  5. Verify that the simplified expression is equivalent to the original equation.

Can you solve a Boolean identity without using the laws of Boolean algebra?

No, the laws and rules of Boolean algebra are essential for solving Boolean identities. Without them, there is no systematic way to manipulate the expression and simplify it.

How can solving Boolean identities be useful in real-life applications?

Boolean identities have various applications in fields such as computer science, electrical engineering, and digital logic design. They allow us to simplify and manipulate logical expressions, which can be used in programming, circuit design, and other areas. In addition, understanding Boolean identities can help us better understand and analyze complex systems and make logical decisions based on given conditions.

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