Symbolised as $P\rightarrow Q,\;P\vee R,\;\sim Q\vdash R$, the argument about flowers and a birthday is:

1. Premise one says a birthday implies flowers: $P\rightarrow Q$. 2. Premise three says no flowers were brought: $\sim Q$. 3. Modus tollens on those two gives $\sim P$ — it was not the birthday. 4. Premise two says $P\vee R$: either the birthday or waking late. 5. Disjunctive syllogism with $\sim P$ forces $R$, so the conclusion follows and the argument is valid. _Source: NECTA ACSEE 2023 Advanced Mathematics 142/2, Question 2: Logic_