Boolean Algebra Identities: How do they work?

[influx]

C) How did they go from the first red line to the second?
f) How did they go from the first green line to the second
g) B + B(bar) = 1, so surely the answer should have a +1 ?

2) How did they go from the first purple line to the second?

I have a list of the Boolean laws and I have used them in about 10 other questions with no problem but I got stuck on these 4.

 

[jedishrfu]

for the green one I was able to verify the step using a boolean table showing that the first green line expression matched the second one.

You could do the same for the others to convince yourself that they are correct.

The red one is probably by definition of XOR

and the blue one is an identity. 0+1=1 or 1+0=1

 

[LCKurtz]

A common identity is $A + \overline A B = A + B$. It makes sense if you think about it and you can prove it like this: $A + \overline AB = (A +AB) + \overline AB = A + (A+\overline A)B =A+B$. If you look at it right, you will see this identity explains the green one.