I've been working on these problems for a week now and with the due date coming up soon I'm throwing myself at the internet's mercy. I'm just starting out in a freshman level design logic class and am having a terrible time with the algebraic manipulation. Any help would be greatly appreciated.
For this question the book has asked me to determine whether the function is valid or not.
1. x'z + xyz' + x'y + xy' = y'z + xz' + yz' + x'yz
Working on the left, in excruciating detail...
x'(z + y) + x(yz' + y') =
x'(z + y) + x(y + z') =
x'z + x'y + xy + xz' =
x'y + xy + x'z + xz' =
y + x'y + xz' =
y + xz'
Working on the right, again, in detail...
y'z + xz' + yz' + x'yz =
z(y' + x'y) + z'(x' + y) =
z(x' + y) + z'(x' + y) =
x'z + yz + x'z' + yz' =
x'z + x'z' + yz + yz' =
x' + y
So they aren't equivalant? If someone could check my work though.
Also, I keep coming up with terms that look like: a'b + ab'. Is there a proof that simplifies that or is that as simple as it gets? <-- nevermind, just read the exclusive or page...
I have two other problems that I'm going to keep working at and may post later if I'm still stuck. So stay tuned? Exciting stuff, I know.
Like I said, any help would be appreciated.
For this question the book has asked me to determine whether the function is valid or not.
1. x'z + xyz' + x'y + xy' = y'z + xz' + yz' + x'yz
Working on the left, in excruciating detail...
x'(z + y) + x(yz' + y') =
x'(z + y) + x(y + z') =
x'z + x'y + xy + xz' =
x'y + xy + x'z + xz' =
y + x'y + xz' =
y + xz'
Working on the right, again, in detail...
y'z + xz' + yz' + x'yz =
z(y' + x'y) + z'(x' + y) =
z(x' + y) + z'(x' + y) =
x'z + yz + x'z' + yz' =
x'z + x'z' + yz + yz' =
x' + y
So they aren't equivalant? If someone could check my work though.
Also, I keep coming up with terms that look like: a'b + ab'. Is there a proof that simplifies that or is that as simple as it gets? <-- nevermind, just read the exclusive or page...
I have two other problems that I'm going to keep working at and may post later if I'm still stuck. So stay tuned? Exciting stuff, I know.
Like I said, any help would be appreciated.
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