NIMCET 2026 — Mathematics PYQ

To determine the number of distinct regions created in a Venn diagram containing $n$ sets, we use the following mathematical principle:

The Rule:

For $n$ sets in a Venn diagram, the universal set is partitioned into $2^n$ distinct regions. Each region corresponds to a specific intersection of the sets and their complements.

Calculation:

In this problem, we are given $n=5$ sets. Applying the formula:

$$\text{Number of regions}=2^n$$

$$\text{Number of regions}=2^5$$

$$\text{Number of regions}=2\times 2\times 2\times 2\times 2$$

$$\text{Number of regions}=32$$

Therefore, a Venn diagram with 5 sets will result in $32$ distinct regions.

Correct Option: 4. 32