logical algebra

[Erros]

Hello everyone, I'm just learning logic, algebra and rules and doing tasks, so I don't know if what I did is the correct solution and good

Using only the rules of Boolean algebra (and nothing else), minimize the Boolean expression
NOTE: The solution is only 3 literals long.

 

[blamocur]

If :
X = True,
Y = False,
Z = False
then one gets False for the original expression but True for your resulting expression. At least this is what my script thinks.

 

[Steven G]

I don't know if what I did is … good

Your very 1st line is wrong.

 

[Erros]

That is ok?

 

[blamocur]

Logical 'and' is commutative, which means that your second answer is identical to the first.

 

[Erros]

Logical 'and' is commutative, which means that your second answer is identical to the first.

Is this done well and correctly, the way to reduce to 3 literals

 

[blamocur]

Is this done well and correctly, the way to reduce to 3 literals

IF your second answer is equivalent to your first answer AND your first answer is incorrect THEN you second answer is incorrect too.

 

[Erros]

Okay, I understood, but I'm asking what I should fix to make it correct?

IF your second answer is equivalent to your first answer AND your first answer is incorrect THEN you second answer is incorrect too.

 

[blamocur]

I could have made mistakes of my own, but it looks like half of your transformations are wrong. In those cases I cannot understand how you get from one line to another. For example, you've modified the first transformation flagged by @Steven G in post #3, but you did not make it right.

My suggestion for you is to write explanations for each transformation so we can check if your understanding of the rules needs corrections. You can start with the first transformation and post it for us to check.

 

[Dr.Peterson]

Does everyone realize that the change from the first answer to the second answer was just that the first line had been wrong at first, and was corrected to match the original statement of the problem?

The answer wasn't changed, only the original form:

​

was wrong​

is right​

I believe the answer (and the work) has been right all along (though I could be missing something).

 

[blamocur]

I believe the answer (and the work) has been right all along (though I could be missing something).

Not sure I agree. While the final answer seems correct the intermediate transformations don't seem so. E.g., in the very first transformation expressions [imath](x\wedge z) \vee (x\wedge \bar y) \vee (\bar z \wedge y)[/imath] and [imath]x \wedge (z \wedge \bar y) \vee (\bar z \wedge y)[/imath] have different values when [imath]x=y=z=T[/imath]

 

[Dr.Peterson]

Not sure I agree. While the final answer seems correct the intermediate transformations don't seem so. E.g., in the very first transformation expressions [imath](x\wedge z) \vee (x\wedge \bar y) \vee (\bar z \wedge y)[/imath] and [imath]x \wedge (z \wedge \bar y) \vee (\bar z \wedge y)[/imath] have different values when [imath]x=y=z=T[/imath]

You're right. I think I was reading it as it was intended, with an or where an and was written, or something like that. (I don't have time at the moment to look carefully.)

 

[blamocur]

(I don't have time at the moment to look carefully.)

I too was too lazy to look carefully, so I wrote a quick script to do the checking

 

[Erros]

I did it in detail and fine, is this now exactly final and are these the 3 literals that are required in this task

 

[blamocur]

I did it in detail and fine, is this now exactly final and are these the 3 literals that are required in this task View attachment 34411