How is this possible???
- Thread starter miiike
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Is the first dash character a "minus" sign, or just the start of a line? What is the relationship between, for instance, A and A'? What is the "law" to which you make reference? Are you working with sets and their complements, with logical statements, or something else?
Please be complete. Thank you! :wink:
I'm sorry, the dash is meant to indicate the start of a line.
No relationship between A and A'.
The law was introduced to me as a hint to solve the above expression.
Im trying to simplify the boolean expression though, but to no avail
I do not understand the question. Are you sure you gave it exactly as given in your text?I'm sorry, the dash is meant to indicate the start of a line.
No relationship between A and A'.
The law was introduced to me as a hint to solve the above expression.
Im trying to simplify the boolean expression though, but to no avail
Any possibility that \(\displaystyle A' \implies \bar{A}\ and\ C' \implies \bar{C}\ ?\) If so:
\(\displaystyle (A + C) * (\bar{A} + B + \bar{C}) = (A * \bar{A}) + AB + A\bar{C} + \bar{A}C + BC + (C * \bar{C}) = 0 + AB + A\bar{C} +\bar{A}C + BC + 0 = AB + A\bar{C} + \bar{A}C + BC \ne\)
\(\displaystyle \bar{A}C + A\bar{C} + AB.\)
(Male OR Democrat) AND (Female OR Young OR Republican) =
Young_Male OR Republican_Male OR Democratic_Female OR Young_Democrat.
To put it even simply, I'm trying to simplify / equate:
(A + C) (A' + B + C') to A'C + AC' +AB
the further i could get was:
AB + AC' + A'C + BC
after simplifying the 1st statement on the left
why do you believe that it can be simplified further?
That's because I was given the hint : XZ + XY + YZ'
to work it out / equate the 1st statement with the 2nd.
Any ideas?
The hint is meaningless. It is not even an equation; it is just an expression.That's because I was given the hint : XZ + XY + YZ'
to work it out / equate the 1st statement with the 2nd.
Any ideas?
I gave you an example to show that what you are trying to prove as true is NOT generally true.
It may be true if there are constraints on A, B, and C, but you have not given any such constraints. Stapel asked you in the first response about relationships or constraints. You said there are none although it is NOW clear that A' and C' were intended as complements of A and C.
If this is a problem from a book, please give it exactly.
I apologise in my lack of understanding to relationships or constraints.
To clarify, this problem act as a 'tool' to further understand boolean theorems.
So if the above statements were meant as boolean expressions, ie. eg. A' as a complement of A,
How would i further simplify it?
Thank you for your patience.
HallsofIvy
Elite Member
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By the "distributive" law for Boolean expressions, (A+ C)(A'+ B+ C')= AA'+ AB+ AC'+ A'C+ BC+ CC'. AA' and CC' are false of course so that reduces to AB+ A'C+ AC'+ BC which is NOT what you have. It does not simplify to A'C+ AC'+ AB unless there is some additional information showing that B and C are contradictory.Hi
can i ask, given the following question:
- (A + C) (A' + B + C'), how can i simplify it to A'C + AC' +AB?
- does the law XZ + XY + YZ' even apply?
Your detailed steps will help a lot. Thanks in advance
Thank you, with your explanation & understanding, I feel more comfy in sharing the full prob.
Anw, i did mention that it was reduced to AB+ A'C+ AC'+ BC in the prev post.
So I'm juz wondering how it may be further reduced to A'C+ AC'+ AB, given the following prob:
Prove that (A + C)(A' + B + C') is congruent to A'C + AC' + AB
I thought the 2nd statement may be easier to start with that's y I started with that.
Any ideas?