Hello all,
This is my first post here as I am new here.

My question is in this proof listed below in the image. I can't understand a line how is this possible in Boolean Algebra.
Any help will be appreciated.

Truth table:

 

X Y | X+X.Y

|

0 0 | 0

0 1 | 0

1 0 | 1

1 1 | 1

 

So X+X.Y = X for every case.

 

Intuitively, if X is true then the result is true (the second term doesn't matter). if X is false, then the second term is false too.

The line you questioned, specifically, is 1+Y = 1. But that's just the definition of logical OR - if either term is true then the OR of the terms is true.

Domination laws(in case required to specify).

 

https://en.wikipedia.org/wiki/Logical_equivalence

Truth table:

 

X Y | X+X.Y

|

0 0 | 0

0 1 | 0

1 0 | 1

1 1 | 1

 

So X+X.Y = X for every case.

 

Intuitively, if X is true then the result is true (the second term doesn't matter). if X is false, then the second term is false too.

The line you questioned, specifically, is 1+Y = 1. But that's just the definition of logical OR - if either term is true then the OR of the terms is true.

Now my doubt is cleared. Thanks for helping.