Question

Prove algebracially that xy+xy'=x

Answer 1

ANSWER................... note- 1• xy=x and y. 2• xy'=x and y'. 3• xy+xy'= xy or xy'. so now it is proved that xy+xy'=x hope this helps you. please mark me as brainliest.

Answer 2

Given:  xy + xy'=x

To find Prove the above expression algebraically.

Solution: The above expression is the example of Boolean Algebra, which is a branch of algebra is that uses binary values(0 or 1), 0 stands for "false" and 1 for "true". In this boolean algebra, it follows and obeys some laws and by the implementation of that laws only we can solve the problems.

Some of the laws are:

1. De Morgan's Law: (x.y)'= x'+y'      [x' is the complement of x and same for y]

                                       (x+y)'= x'.y

    2. Complementarity Law: x+x'=1

                                               x.x'=0    

     3. Identity Law:  x+0=x

                                 x.1=x

Now from above, we have

xy + xy'=x

L.H.S,

xy + xy'

=x(y+y')   [Taking x common from the expression]

=x.(1)       [Implementing complementarity law]

=x = R.H.S

Hence L.H.S= R.H.S, so therefore the expression xy + xy'= x is proved algebraically.