# Thread: Show that A + 0 = A

1. ## Show that A + 0 = A

Just a simple question I want to know how to do, google hasn't been a help.

Show that A + 0 = A

Is it something like, make A a 1 so its 1 + 0 = 1?

2. Originally Posted by gary223
Just a simple question I want to know how to do, google hasn't been a help.

Show that A + 0 = A

Is it something like, make A a 1 so its 1 + 0 = 1?
You need to be more specific now. What is A, 0, +? I presume there is nothing to prove here. It is an assumption we start with. And the above holds by definition of 0.

3. For all A

A+0=A

Kind of self obvious but to prove like less obvious equalities perhaps the below is helpful

Transpose to A-A=0

4. Originally Posted by gary223
Just a simple question I want to know how to do, google hasn't been a help.

Show that A + 0 = A

Is it something like, make A a 1 so its 1 + 0 = 1?
Is A a matrix? If so, are you working over arbitrary field, over reals...?

Nevertheless, to verify this for matrices you just have to look at each position, you get equality $\displaystyle a_{i,j}+0=a_{i,j}$, which is valid in any field (in particular, in reals).

However, it was just a guest that you mean matrices - you should have specified the context of your question.

5. Its not a matrix. I'd imagine it has something to do with Boolean algebra?

6. Originally Posted by gary223
Its not a matrix. I'd imagine it has something to do with Boolean algebra?
How about $\displaystyle A\vee 0=A\vee \left(A\wedge \neg A\right)=A$ by the absorption property?

7. Originally Posted by gary223
Its not a matrix. I'd imagine it has something to do with Boolean algebra?
You imagine? This is your problem! Where did you get it? What algebraic system are you in?