Let $\{$O$1,$ O$2,$ O$3,$ O$4\}$ represent the outcome of a random experiment, with

P$(\{$O$1\})=$P$(\{$O$2\})=$P$(\{$O$3\})=$P$(\{$O$4\}).$ Consider the following events: P$=\{$O$1,$O$2\},$

Q$=\{$O$2,$O$3\},$ R$=\{$O$3,$O$4\},$S$=\{$O$1,$O$2,$O$3\}.$

Then, which of the following statements is true?

$($A$)$ P and Q are independent

$($B$)$ P and Q are not independent

$($C$)$ R and S are independent

$($D$)$ Q and S are not independent