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1 Apr 2009, 11:31 PM
| #1 (permalink) |
| Executive Member  HSC: 2008 Gender: Male Location: Melbourne
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19 Nov 2009, 4:46 PM  | Boolean algebra question You can hide this advertisement by registering. Ey guys, having abit of trouble with a question as was wondering if any1 could give me the answer to it plus the working out.The question is: Use the axioms (a)-(j) and the properties (k)-(u) to prove that in every Boolean algebra /(x+y/z) = /x/y/z + /x/yz + /xyz [where the slash infront of a term means "x bar" or "x compliment".] Justify each line of your proof idicating what axiom/property you use. I can kinda of do it, but i never get /x/y/z + /x/yz + /xyz as my answer.
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1 Apr 2009, 11:53 PM
| #3 (permalink) |
| Executive Member HSC: 2008 Gender: Male Location: Melbourne
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19 Nov 2009, 4:46 PM | Re: Boolean algebra question meh i couldnt figure out where to put it...it wouldn't go in science and engineering because this comes under discrete maths so i just took a guess.
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2 Apr 2009, 1:56 AM
| #4 (permalink) |
| Premium Member  HSC: 2004 Gender: Male
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Yesterday, 3:30 AM Blog Entries: 1   | Re: Boolean algebra question /(x+y/z) = /x/y/z + /x/yz + /xyz Use apostrophes. (x + yz')' = x'(yz')' (de Morgans) = x'(y'+z) (de Morgans) = x'y' + x'z (distributive) = x'y'*1 + x'z*1 (identity) = x'y'(z+z') + x'z(y+y') (a+a'=1) = x'y'z + x'y'z' + x'zy + x'zy' (distributive) = x'y'z + x'y'z' + x'yz + x'y'z (commutative under multiplication) = (x'y'z + x'y'z) + x'y'z' + x'yz (commutative under addition) = x'y'z + x'y'z' + x'yz (a + a = a) = x'y'z' + x'y'z + x'yz (commutative under addition)
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2 Apr 2009, 3:34 PM
| #5 (permalink) |
| Premium Member HSC: 2004 Gender: Male
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Yesterday, 3:30 AM Blog Entries: 1 | Re: Boolean algebra question There's also a few times I used the associative law in there, but you can figure that one out.
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26 Jul 2009, 9:11 PM
| #6 (permalink) | |
| Assistant Member HSC: 2008 Gender: Male
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Yesterday, 12:41 PM | Re: Boolean algebra question Quote:
and Boolean algebra is used alot in computer science. Look to the appendix section of any algorithm analysis/design or theory of computation book and there should be a section on boolean algebra. Also many early computer science courses have a section on logic, including boolean algebra. For example 'Discrete structures' at melbourne uni. This is definently the right place for such a question  | |
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