What does the star symbol means in the binary operation a*b .... Ex: x*y=x+y+xy

Question

what does the star symbol means in binary operation algebra (logic) Does it refer to a certain rule

Answer 1

It means the operation defined on the RHS.

For example $$2*3= 2+ 3+2\times 3=11$$

Answer 2

I doesn't refer to a certain rule, it refers to the particular rule defined at the moment.

Answer 3

No.

In your example $x*y$ is being defined to mean the binary operation: $x+y+xy$. (Presumably so you can solve some problem about such a binary operation.)

In another problem you might be told $x*y$ means something else. Or in general we can say "Let $*$ be a binary operation" and we won't know anything about what $x*y$ is; just that it is some binary operation.

Answer 4

In binary logic $+$ refers to OR and $\cdot$ refers to AND.

You could also use alternate notation $x\lor y\lor(x\land y)$ but it is equivalent to simple $x\lor y$ or $x+y$ in the origninal notation.

Assuming it is really a logical operation, I do not see the purpose of defining $*$ if it is the same thing as $+$ or maybe this is th epurpose of the exercise to show they are the same rules.

Anyway, I sometimes saw $*$ being used for NAND i.e. $\lnot(x\land y)$ or $(xy)'$ in both notations.

But this is not the case here, are you certain about the definition of $x*y$ ?

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