Q.A die is thrown once. Let $A$ be the event 'the number is even' and $B$ be the event 'the number is greater than $4$'. Write $A$, $B$, $A \cup B$ and $A \cap B$ as subsets of the sample space.

[!TLDR] Translate each description into a subset of $S=\{1,\dots,6\}$, then apply union/intersection. [!ANSWER] $A=\{2,4,6\}$, $B=\{5,6\}$, $A\cup B=\{2,4,5,6\}$, $A\cap B=\{6\}$.

The sample space for one die is $S = \{1,2,3,4,5,6\}$. 'The number is even' selects $A = \{2,4,6\}$. 'The number is greater than $4$' selects $B = \{5,6\}$. For $A \cup B$ (the number is even OR greater than $4$), combine all elements appearing in either set: $\{2,4,6\} \cup \{5,6\} = \{2,4,5,6\}$. For $A \cap B$ (the number is even AND greater than $4$), keep only elements common to both: the only number that is both even and greater than $4$ is $6$, so $A \cap B = \{6\}$. [!ANSWER] $A=\{2,4,6\}$, $B=\{5,6\}$, $A\cup B=\{2,4,5,6\}$, $A\cap B=\{6\}$.

Write $A$ and $B$ as explicit subsets of $S$ first, then form $A \cup B$ by combining all elements and $A \cap B$ by keeping only common elements.

A common mistake is swapping union and intersection — remember $\cup$ ('or') generally gives a larger set than either $A$ or $B$ alone, while $\cap$ ('and') gives a smaller (or equal) set.