Step 1: Compound \(P\) reacts with bromine water (indicating unsaturation) and gives a positive iodoform test (presence of methyl ketone or alcohol).
Step 2: \(P\) on ozonolysis gives \(Q\) and \(R\), where \(Q\) gives a positive iodoform test, indicating the presence of a methyl ketone. \(R\) does not give the iodoform test, indicating the absence of a methyl ketone group.
Step 3: Oxidation of \(Q\) and \(R\) with PCC yields \(S\) and \(T\), which both give positive iodoform tests, indicating the presence of \(CH_3CO\) groups.
The structures of \(S\) and \(T\) contain 1 oxygen atom each, giving a total of:
\[
\text{Total number of oxygen atoms in \(S\) and \(T\): 2.}
\]