I was reading the distributive law of sets (I keep coming back to basic maths when needed, forget it after some time, then come back again. Like I'm in loop):
$A\cup(B \cap C)=(A\cup B)\cap(A\cup C)$
The proof (which I'm assuming everyone knows) has a transaction between lines which baffled me , which are:
$x \in A$ or ($x\in B$ and $x\in C$)
($x\in A$ or $x\in B$) and ($x\in A$ or $x \in C$)
in the second line, did they just applied distributive law? (in the proof of distributive law itself Oo) or Did they simple assumed "and" = "+" etc like following:
$2 X (A + B) \equiv (2XA) + (2XB)$
Another question will be :
($x\in A$ or $x\in B$) or $x\in C\implies x\in A$ or ($x\in B$ or $x\in C$)
I can just open the brackets?