Question

Boolean QUestion
how come
x'z + xy + yz = xy + x'z

Answer 1

this boolean calculator says they are equivalent (same truth table)

Answer 2

http://www.wolframalpha.com/widgets/view.jsp?id=a52797be9f91295a27b14cb751198ae3

Answer 3

i dont see how the left side equals right side,

Answer 4

using a proof

Answer 5

@perl
XY+(X+X')YZ+X'Z=XY+XYZ+X'YZ+X'Z=XY(1+Z)+X'(1+Y)Z
=XY+X'Z

Answer 6

because (X+X') = 1 , and 1 * x = x

Answer 7

@gorv
why does XY(1+Z)+X'(1+Y)Z =XY+X'Z

Answer 8

1+x = 1

Answer 9

1+x= 1

Answer 10

thanks :)

Answer 11

@gorv
how did you know to do this?

Answer 12

very nice proof

Answer 13

oh , let me check

Answer 14

he told me that
(x'z'+xy')' = z(x'+y) which is false

Answer 15

he said that is the book answer

Answer 16

i see, i went too fast

Answer 17

so what were you saying before, that we have to find MMF form. what was your approach?

Answer 18

you dont need my permission :)

Answer 19

ok i misunderstood what he said, i read it too fast

Answer 20

in kert question, it asked to simplify. so , yours is good

Answer 21

anyway, you got more than him

Answer 22

me too. sit here to learn from others, :)

Answer 23

so we wanted minimal sum of products form.
and you can do it as gorv did it, or use karnaugh map

Answer 24

i dont know how to do karnaugh map

Answer 25

yeap, to 4 variable problem, I prefer K map

Answer 26

google

Answer 27

I studied it by myself. quite easy

Answer 28

did you know the solution gorv did?

Answer 29

sure, I studied that way from my prof

Answer 30

how come gorv answered and you didnt?

Answer 31

because I ammmmm brainless. hehehe

Answer 32

haha

Answer 33

all is good ,
so how come xy + yz + x'z is not minimal form? because y repeats

Answer 34

go to other topic friend, boolean is not hard to understand. the question ask about arithmetic is amazing and the guy gave out the answer is a real big guy.

Answer 35

can you give me link?

Answer 36

remember the question asked about a =9 mod 10
a =8 mod 9....
amazing answer.

Answer 37

you were there, and both us thought about chinese theorem

Answer 38

it turns out we didnt need it because there was a trick

Answer 39

of course our ways can come up with that solution, but his way is..... Perfect

Answer 40

Solve
x mod 10 = 9
x mod 9 = 8
x mod 8 = 7
x mod 7 = 6
x mod 6 = 5
x mod 5 = 4
x mod 4 = 3
x mod 3 = 2
x mod 2 = 1

Answer 41

not a trick, just flexibility what we don't have

Answer 42

now watch my solution

Answer 43

yeah, to me, meet that problem, I have to figure out phi function to solve

Answer 44

if this is true :
x mod 10 = 9
x mod 9 = 8
x mod 8 = 7
x mod 7 = 6
x mod 6 = 5
x mod 5 = 4
x mod 4 = 3
x mod 3 = 2
x mod 2 = 1

Then this is true:
x mod 10 = 9 mod 10
x mod 9 = 8 mod 9
x mod 8 = 7 mod 8
x mod 7 = 6 mod 7
x mod 6 = 5 mod 6
x mod 5 = 4 mod 5
x mod 4 = 3 mod 4
x mod 3 = 2 mod 3
x mod 2 = 1 mod 2

Then this is true:

x +1 mod 10 = 9 +1 mod 10 = 0
x +1 mod 9 = 8 +1 mod 9 = 0
x +1 mod 8 = 7 +1 mod 8 = 0
x +1 mod 7 = 6 +1 mod 7 = 0
x +1 mod 6 = 5 +1 mod 6 = 0
x +1 mod 5 = 4 +1 mod 5 = 0
x +1 mod 4 = 3 +1 mod 4 = 0
x +1 mod 3 = 2 +1 mod 3 = 0
x +1 mod 2 = 1 +1 mod 2= 0

Answer 45

ok so far?

Answer 46

good

Answer 47

so x+1 is a multiple of 2,3,4,5,6,7,8,9,10
and we want the smallest multiple
x+1 = LCM { 2,3,4,5,6,7,8,9,10}

Answer 48

just notation, x+1 = 0 mod 10 for example. not as yours. but I understand

Answer 49

x +1 mod 10 = 9 +1 mod 10 = 0 mod 10
x +1 mod 9 = 8 +1 mod 9 = 0 mod 9
x +1 mod 8 = 7 +1 mod 8 = 0 mod 8
x +1 mod 7 = 6 +1 mod 7 = 0 mod 7
x +1 mod 6 = 5 +1 mod 6 = 0 mod 6
x +1 mod 5 = 4 +1 mod 5 = 0 mod 5
x +1 mod 4 = 3 +1 mod 4 = 0 mod 4
x +1 mod 3 = 2 +1 mod 3 = 0 mod 3
x +1 mod 2 = 1 +1 mod 2= 0 mod 2

Answer 50

Actually, for this part, I studied last summer when I was free from math at school and unfortunately, I studied by myself. I didn't have a prof confirm what I have.

Answer 51

so we used a theorem
x mod n = y mod n if and only of ( x + c) mod n = ( y + c ) mod n

Answer 52

yep

Answer 53

and also we can say
(x +1 ) mod 10 = 0 means that (x+1) / 10 = k , (because no remainder) (x+1) is a multiple of 10

Answer 54

(x+1) = 10*k

Answer 55

got it

Answer 56

so we want a multiple of 10, a multiple of 9, a multiple of 8 ,... and might as well use the least common multiple.
the problem didnt actually specify the 'least' , but

Answer 57

also the original problem excluded x+1 mod 9, x+1 mod 7, etc

Answer 58

its a nice problem , yes i didnt see the solution. but its ok

Answer 59

come here http://openstudy.com/study#/updates/517bedc0e4b0249598f7b180
I saw that problem once, let see how other answer

Answer 60

@perl
yeah 1+anything =1
that XX'=0 and gate
X+X'=1 or gate

Answer 61

gorv, i wasnt sure how you discovered the proof (but the proof works :)

Answer 62

the main thing was to eliminate YZ so i apply bolean operation

Answer 63

interesting