Prove that in boolean algebra the cancellation law does not hold,that is, show t

Question

Prove that in boolean algebra the cancellation law does not hold,that is, show that, for every x,y, and z in a Boolean algebra,xy=xz does not imply y=z. Does x+y=x+z imply y=z?
Please help, I have a hard time with boolean algebra since Ido not manipulate the postulates and identities correctly. I willrate you well if you show me how to do this.
Please help, I have a hard time with boolean algebra since Ido not manipulate the postulates and identities correctly. I willrate you well if you show me how to do this.

Explanation / Answer

Boolean algebra x+y=x+z imply y=z :

Using truth table:

    

x    y      z       x+y        x+z

0      0     0        0           0

0      1      1        1          1

1      0       0        1          1

1       1         1       1         1

Check the above truth table Both Y, Z=0 or Y, Z=1 with differentX values.

      Observe the X+Y and X+Zvalues imply Y=Z

                         We got Equal values where Y=Z.

So the above statement is correct.

Still u have any doubts cramster is there.

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