# An other Boolean's Algebra question

Discussion in 'Homework Help' started by kelvinmacks, Dec 20, 2014.

1. ### kelvinmacks Thread Starter New Member

Dec 15, 2014
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hi , i have one more example here involving 3 variables , X , Y , Z . i am having problem with the SOP and POS here.
i. ) for the SOP , why the X , Y AND Z can be false at the same time? As you can see it , the SOR contains X'Y'Z'
ii. ) For the POS , why it contain XYZ ? didn't you say that XYZ can be true at the same time?

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2. ### WBahn Moderator

Mar 31, 2012
18,085
4,917
You should start a new thread with a new problem. Otherwise you will get responses to each all mixed together and it will become chaos. I'll report your post to the mod team who will split off the new problem into a new thread, so don't worry about it.

If X is False, Y is False, and Z is False, then you want F to be True. So that means that the minterm that covers that combination needs to be included in the SOP equation. Remember, in the standard SOP form, there is exactly one minterm for each combination of inputs that should yield a True output, all of which are ORed together.

Similarly, in the standard POS form, there is exactly one maxterm for each combination of inputs that should yield a False output, all of which are ANDed together.

I don't understand your second question. Of course X, Y, and Z can be true at the same time. But that has no bearing on whether the output of the function should be True of False for that combination -- that is defined by the truth table for the function.

Now, for that second problem, count up how many minterms there are in their SOP expression. Does this match the number of rows for which the function is supposed to be True? If not, which one(s) do(es)n't match? Ask a similar question for the POS expression?

Are you sure that the expressions below the table are for the function defined by the table? If that's the case, you might consider getting a different book. While all books have errors, there comes a point where the errors are too extensive to continue bothering with.

3. ### kelvinmacks Thread Starter New Member

Dec 15, 2014
19
0
why the book is giving F(X , Y, Z ) = X'Y'Z' +X'YZ +XY'Z +XYZ'
Shouldn't be the F(X,Y,Z ) be any one of the 8 possible outcomes(minterm) ?

Apr 5, 2008
15,798
2,384
Hello,

Please start a new threda when you have an other question.
For now I moved these post from this thread:

Bertus

5. ### JWHassler Member

Sep 25, 2013
204
34
You need a new book! The posed problem shows a truth table with three 'true' results and the answer has four of them summed.

The inputs X,Y and Z can be false at the same time: they can have any of eight possible values.
A truth-table specifies the output for every one of those eight values. Only some of those outputs are 'true': those values are included in the equation.

6. ### kelvinmacks Thread Starter New Member

Dec 15, 2014
19
0
So can you please tell me what should the F(X, Y) for the above question?

7. ### WBahn Moderator

Mar 31, 2012
18,085
4,917
You should be able to take a pretty good shot at it by now.

Identify the rows in the truth table for which the output of the function should be True.

OR together the minterms for those rows (and only those rows).