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 9 months ago
simplify the following using Boolean algebra.
(xy)'+xz'+yz
a)y+z'
b)x+y
c)X'+y
d)xz'
 9 months ago
simplify the following using Boolean algebra. (xy)'+xz'+yz a)y+z' b)x+y c)X'+y d)xz'

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ybarrap
 9 months ago
Best ResponseYou've already chosen the best response.1$$ \Large{ (xy)'+xz'+yz\\ =[(xy)(xz')'(yz)']'\\ =[(xy)(x'+z)(y'+z')]'\\ =[((xyx')+(xyz))(y'+z')]'\\ =[0+xyzy'+xyzz']'\\ =[0+0+0]'\\ =[0]'\\ =1 } $$ This is a tautology, because it is always true. Here is another method using a Truth Table dw:1395590669537:dw This also shows a tautology

AkashdeepDeb
 9 months ago
Best ResponseYou've already chosen the best response.1(xy)' + xz' + yz We know that (xy)' = x' + y' [De morgan's laws] x' + y' + xz' + yz x' + z' + y' + z x' + y' + 1 = 1 None of the options are as 1 @ybarrap Is truth table the only method to find that out?

AkashdeepDeb
 9 months ago
Best ResponseYou've already chosen the best response.1@moli1993 I guess you have to see which of the options also show Tautology [Always true].

ybarrap
 9 months ago
Best ResponseYou've already chosen the best response.1The truth table is authoritative. This is a tautology. None of the options are a tautology so they are all incorrect.

moli1993
 9 months ago
Best ResponseYou've already chosen the best response.1I am so sorry , wrote the wrong question here : it is (xz)'+xz'+yz and the options are same as given earlier !

moli1993
 9 months ago
Best ResponseYou've already chosen the best response.1process is same but it's not a tautology i suppose !

dumbcow
 9 months ago
Best ResponseYou've already chosen the best response.0(xz)' = x' + z' z' +xz' = z'(1+x) = z' > x' + z' + yz = x' +z' +z = x' + 1 = 1

moli1993
 9 months ago
Best ResponseYou've already chosen the best response.1how x' + z' + yz = x' +z' +z

AkashdeepDeb
 9 months ago
Best ResponseYou've already chosen the best response.1(xz)'+xz'+yz We know that (xz)' = x' + z' [De morgan's laws] x' + z' + xz' + yz x' + (z' + xz') + yz [ In z' + xz' take z' common, z'(1+x) = z'(1) = z' ] x' + z' + yz [yz = zy] z' + zy + x' Using simplification law [A + A'B = A+B] we get, z' + y + x' Final answer should be x' + y + z'

moli1993
 9 months ago
Best ResponseYou've already chosen the best response.1but it doesnt matches any of the options given above

AkashdeepDeb
 9 months ago
Best ResponseYou've already chosen the best response.1(xz)' + y I am pretty sure, this is the final answer. :/ @ybarrap @dumbcow ?

moli1993
 9 months ago
Best ResponseYou've already chosen the best response.1me too I think u r correct !

dumbcow
 9 months ago
Best ResponseYou've already chosen the best response.0yep http://www.wolframalpha.com/input/?i=~%28x+and+z%29+or+%28x+and+~z%29+or+%28y+and+z%29

moli1993
 9 months ago
Best ResponseYou've already chosen the best response.1Thank you all for helping me !
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