Let $\#$ be the binary operator defined as
$X\#Y = X'+Y'$ where $X$ and $Y$ are Boolean variables.
Consider the following two statements.
- $(S_1)$ $(P\#Q)\#R = P\#(Q\#R)$
- $(S_2)$ $Q\#R = (R\#Q)$
Which are the following is/are true for the Boolean variables $P, Q$ and $R$?
- Only $S_1$ is true
- Only $S_2$ is true
- Both $S_1$ and $S_2$ are true
- Neither $S_1$ nor $S_2$ are true