Q.In a market survey of 120 customers of an Odisha handicrafts store, 70 customers purchase textile products, 50 purchase pottery products, and 25 purchase both. Find

Add the two individual counts and subtract the overlap once, since it was counted twice; the leftover customers, if any, form the "neither" group.

Step 1 — Identify the sets. Let $A$ = customers buying textile products, $n(A)=70$; $B$ = customers buying pottery products, $n(B)=50$; $n(A \cap B) = 25$ (buy both). Total surveyed $= 120$.

Step 2 — Apply the inclusion-exclusion formula.

So 95 customers buy at least one of the two products.

Step 3 — Find the "neither" group. Customers buying neither product lie outside $A \cup B$: $120 - 95 = 25$. …

Building the Venn-diagram breakdown (only-A, only-B, both, neither) directly and adding the four regions is an equally vali …

Adding $70+50=120$ and stopping there double-counts the 25 customers who buy both — the overla …