is this boolean algebra transformation correct

Question

I have the following expression:
(A=1 or A=2) or (B=1 or B=2)
and try to transfer it to:
(A=1 or A=2 or B=1 or B=2)
Are these two expressions equal?

Answer 1

Logical or is an associative operation. That implies that it doesn't matter how you group things in parentheses—if you're oring them all together they will come out the same. That's why the notation without parentheses is allowed at all. I think you should probably also have an intuitive sense of the meaning of those statements that should guide you.