If R is $\sigma -$ring then {$E\in X|E\in R \text { or} \ E^c \in R$ } is a $\sigma$ -algebra
$\sigma -$ring : A family of sets $R\in P(X)$ is called a $\sigma $-ring if it is closed under countable unions and differences of 2 sets.
$\sigma-$ algebra: A family of sets $R\in P(X)$ is called a $\sigma- $algebra if it is closed under countable unions and every element has a complement in it.
I had proved that it is enough to show that if $X\in R$ then $R$ is a $\sigma-$ algebra
Case 1) If $E,E^c\in R$ then by union we are done.
Case 2) If only either $E$ or $E^c \in R,$
then I am not able to proceed.
I wanted to solve this. Please give me only a hint.
Thanks in advance.