Q.Let $A = \{a, b, c, d\}$ and $B = \{c, d, e, f\}$. Verify the commutative properties $A \cup B = B \cup A$ and $A \cap B = B \cap A$ by listing both sides independently.

Compute each side of both equations separately, in the order given, and check that swapping the set order genuinely produces identical results.

Step 1 — Compute $A \cup B$. Combine every element of $A=\{a,b,c,d\}$ and $B=\{c,d,e,f\}$, listing shared elements once: $A \cup B = \{a,b,c,d,e,f\}$.

Step 2 — Compute $B \cup A$ independently. Combine every element of $B$ and $A$ the same way: $B \cup A = \{c,d,e,f,a,b\}$, which — since order of listing inside a set doesn't matter — is exactly $\{a,b,c,d,e,f\}$, the same as Step 1.

Step 3 — Compute $A \cap B$. Elements common to both: only $c$ and $d$ appear in both lists. $A \cap B = \{c,d\}$.

Step 4 — Compute $B \cap A$ independently. The same check, sets swapped: elements common to $B$ and $A$ are still exactly $c$ and $d$. $B \cap A = \{c,d\}$, matching Step 3. …

Treating $B \cup A$ or $B \cap A$ as if they need not be checked separately, simply assuming commutativity without actually re-deriving both sides — the syllabus explicitly asks for VERIFICATION, meaning b …