Hello,
Im trying to understand boolean algebra, I have to do the next problem using Boolean algebra and Identities for this one:


can somebody help me how to do this Im really new to this topic and I dont have any idea how to start

 

So far this what I got:
A + /A (A+B) = A + B
A + /AA + /AB = A+B
A + A + /AB = A + B
A + A + B = A + B <-- I think A + A = A so ..
A + B = A + B <-- Im not sure what to do after this

 

So far this what I got:
A + /A (A+B) = A + B
A + /AA + /AB = A+B
A + A + /AB = A + B
A + A + B = A + B <-- I think A + A = A so ..
A + B = A + B <-- Im not sure what to do after this

What could there be left to do other than move on to the next problem?

You are trying to prove that the left-hand side (LHS) is equal to the right-hand side (RHS). You proceeded to manipulate the LHS until it is identical to the RHS. Congrats.

Proof complete. Assuming it is correct and this one isn't (but it's close)

About the only thing more you could do is to identify which identity you used at each step of the proof and you should only use one identity per line.

There are different styles for doing proofs. What I use below is simply the one I am most comfortable with.

PROVE:
A + B = A + /A (A+B)

PROOF:
   A + B = A + /A(A + B)
1)       = A + /AA + /AB  Distibutivity of AND over OR
2)       = A + A + /AB    <== PROBLEM. /AA is not equal to A, it is equal to 0
3)       = A + /AB        Indempotence
4)       = A + B          <== Do you have an identity that goes from (3) to (4)? If not, do it step by step

The identity that A+A=A is called "imdempotence".

The path you chose is valid (needs some cleaning), but consider that your RHS is A+B and you already have (A+B) on the LHS. Try to see if you can keep that intact and make the other stuff go away.

 

What could there be left to do other than move on to the next problem?

You are trying to prove that the left-hand side (LHS) is equal to the right-hand side (RHS). You proceeded to manipulate the LHS until it is identical to the RHS. Congrats.

Proof complete. Assuming it is correct and this one isn't (but it's close)

About the only thing more you could do is to identify which identity you used at each step of the proof and you should only use one identity per line.

There are different styles for doing proofs. What I use below is simply the one I am most comfortable with.

PROVE:
A + B = A + /A (A+B)

PROOF:
   A + B = A + /A(A + B)
1)       = A + /AA + /AB  Distibutivity of AND over OR
2)       = A + A + /AB    <== PROBLEM. /AA is not equal to A, it is equal to 0
3)       = A + /AB        Indempotence
4)       = A + B          <== Do you have an identity that goes from (3) to (4)? If not, do it step by step

The identity that A+A=A is called "imdempotence".

The path you chose is valid (needs some cleaning), but consider that your RHS is A+B and you already have (A+B) on the LHS. Try to see if you can keep that intact and make the other stuff go away.

I dont understand so I didnt wrong how I am suppose to do it in a differnet way :/

 

I dont understand so I didnt wrong how I am suppose to do it in a differnet way :/

I'm not sure I understand what you are trying to say or ask. Please rephrase it and let's try again.

 

sorry I wrote quickly , so my answer is not right? what do I meant to do ? I cant thing of a new way to do it

 

In going from your second line to your third line:

A + /AA + /AB = A+B
A + A + /AB = A + B

You seem to be claiming that /AA = A

Is that the claim you are making?

Is that a true claim?

In the transition from your third line to your fourth:

A + A + /AB = A + B
A + A + B = A + B

You make the /A go away from the third term. It's not clear the basis upon which you are doing this. I'm not saying it is wrong, I'm saying it is not clear which identity you are using. That's why you should list the identity next to each line.

Most tables of Boolean Identities do not list A+/AB = A+B as an identity. If your's does, great. Write the name of the identity next to that step and you are good. If it isn't listed as an identity, then you can't use it in your proof and you have to carry out the steps explicity.

 

In going from your second line to your third line:



You seem to be claiming that /AA = A

Is that the claim you are making?

Is that a true claim?

In the transition from your third line to your fourth:



You make the /A go away from the third term. It's not clear the basis upon which you are doing this. I'm not saying it is wrong, I'm saying it is not clear which identity you are using. That's why you should list the identity next to each line.

Most tables of Boolean Identities do not list A+/AB = A+B as an identity. If your's does, great. Write the name of the identity next to that step and you are good. If it isn't listed as an identity, then you can't use it in your proof and you have to carry out the steps explicity.

Wait I did wrong this step /A . A = 0 isnt? because that is a boolean Identity so

A + 0 + /A b = A + B

NOW I found in my boolean identity
A + /A b = A + B so whats wrong?

 

Wait I did wrong this step /A . A = 0 isnt? because that is a boolean Identity so

A + 0 + /A b = A + B

Good.

NOW I found in my boolean identity
A + /A b = A + B so whats wrong?

Nothing. As I said, if that is in the table of identities that you are allowed to use for your proofs, great. It is not in many tables (it's in none of the ones I have access to right now). But you should still identity which of the identities you are using next to each step.