# Boolean algebra problem

#### blam50

Joined Mar 8, 2018
4
I am working on problem 9. I do not understand the answer given.

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#### WBahn

Joined Mar 31, 2012
26,486
Which part of the answer do you not understand?

#### blam50

Joined Mar 8, 2018
4
Which part of the answer do you not understand?
Isn't (A + A') equal to 1?

#### WBahn

Joined Mar 31, 2012
26,486
Isn't (A + A') equal to 1?
Yes. And that's how I would have approached it. But notice that going that route the third line would have been

1 · (A·B)

It's not obvious to me how they got from the second to their third line in a single step.

What does your text define the Law of Complementation to be?

I can't imagine it being enough to fill in the gap.

To get to their third step, it would seem like you need to go through deMorgan plus a couple of steps. Or "multiply it out" to get it in SOP form, but that is even more convoluted to get it to that form.

My guess is that the author (or the grad student getting paid to do the solutions) messed up. The end result is correct, but the proof seems invalid.

#### blam50

Joined Mar 8, 2018
4
Yes. And that's how I would have approached it. But notice that going that route the third line would have been

1 · (A·B)

It's not obvious to me how they got from the second to their third line in a single step.

What does your text define the Law of Complementation to be?

I can't imagine it being enough to fill in the gap.

To get to their third step, it would seem like you need to go through deMorgan plus a couple of steps. Or "multiply it out" to get it in SOP form, but that is even more convoluted to get it to that form.

My guess is that the author (or the grad student getting paid to do the solutions) messed up. The end result is correct, but the proof seems invalid.
Complementation law is A+A' = 1
AA' = 0
DeMorgan's is not covered until the next section. This is an online course that I am studying on my own so I cannot get any help from office that runs it. How do you get to the answer given in the book? Thank you for your help.

#### WBahn

Joined Mar 31, 2012
26,486
Complementation law is A+A' = 1
AA' = 0
That's what I expected -- that's the usual meaning.

DeMorgan's is not covered until the next section. This is an online course that I am studying on my own so I cannot get any help from office that runs it. How do you get to the answer given in the book? Thank you for your help.
I actually messed up earlier when I said their result was correct. It isn't. There was a smudge on my computer screen which, combined with my failing vision, made me think their end result was A+B and not A·B. We can tell that their answer is wrong because the original expression is TRUE if A is TRUE regardless of the value of B. That is NOT the case for their result.

While it's certainly possible the person doing the solutions just screwed up, it's also possible that the problem changed from one version of the book to another and whoever updated the solutions only got the first two lines corrected. They may have thought it was right from there on based only on a glance or they may have gotten interrupted part way through and thought they had finished it when they returned to the task. Keep in mind that the folks doing the solutions are being paid next to slave wages and have their own course and research loads that take priority, so this kind of stuff is crammed in late at night and usually shortly after the author starts throwing a temper tantrum because they're starting to catch flak from their publisher about a submission deadline that is fast approaching.

#### blam50

Joined Mar 8, 2018
4
That's what I expected -- that's the usual meaning.

I actually messed up earlier when I said their result was correct. It isn't. There was a smudge on my computer screen which, combined with my failing vision, made me think their end result was A+B and not A·B. We can tell that their answer is wrong because the original expression is TRUE if A is TRUE regardless of the value of B. That is NOT the case for their result.

While it's certainly possible the person doing the solutions just screwed up, it's also possible that the problem changed from one version of the book to another and whoever updated the solutions only got the first two lines corrected. They may have thought it was right from there on based only on a glance or they may have gotten interrupted part way through and thought they had finished it when they returned to the task. Keep in mind that the folks doing the solutions are being paid next to slave wages and have their own course and research loads that take priority, so this kind of stuff is crammed in late at night and usually shortly after the author starts throwing a temper tantrum because they're starting to catch flak from their publisher about a submission deadline that is fast approaching.
I can't thank you enough for your help. I went to my local community college for help today and they thought then answer was incorrect also. Your clear explanation about what might have happened here makes a lot of sense and now I can enjoy my weekend without this problem going around and around in my head!! Thanks a million again!!!!!!!

#### xed_over

Joined Feb 5, 2018
19
you might try Googling for the title of your book, and "errata"... there might have been corrections published