Q.If $A = \{a,e,i,o,u\}$ and $B = \{a,b,c,d,e\}$, find $A \cup B$, $A \cap B$ and $A - B$.

Union combines every element from either set once; intersection keeps only the shared letters; the difference keeps only what belongs to $A$ but not $B$.

Step 1 — Union. Combine every letter from $A$ or $B$, counting shared letters once: $A \cup B = \{a,b,c,d,e,i,o,u\}$ — 8 letters.

Step 2 — Intersection. Letters in both lists: $a$ and $e$ appear in both $A$ and $B$. So $A \cap B = \{a,e\}$.

Step 3 — Difference $A-B$. Letters in $A$ but not $B$: removing $a,e$ (also in $B$) from $A=\{a,e,i,o,u\}$ leaves $\{i,o,u\}$. …

The inclusion-exclusion count $n(A)+n(B)-n(A\cap B)$ gives an independ …

Listing a shared element twice inside the union (e.g. writing $a$ twice) — a set never repeats an element …