Q.Let $S = \{1, 2, 3, 4, 5, 6\}$ and $E = \{1, 3, 5\}$, then $\bar{E}$ is _________.

The idea in plain words

Think of your two favourite groups of friends — the ones who play cricket and the ones who play football. Some friends are in both groups, some in only one, and some in neither. Set operations are simply the mathematical ways to answer questions like: "Who's in at least one team?" or "Who's only in the cricket team?".

The whole secret? Each operation is just a different way of combining or comparing two collections — like sorting your friends into different buckets.

Why this works

Sets are just labelled buckets that hold distinct items. The universal set $U$ is the "whole world" of things we're talking about — say, all your friends. Then each operation picks out a specific bucket:

Step by step

Let's take two concrete sets so you can see each operation in action:

Step 1: Union — gather everything from both, but don't repeat anything.

Step 2: Intersection — only what's common to both.

Step 3: Difference ($A$ minus $B$) — start with $A$, remove anything that's also in $B$.

Step 4: Complement — needs a universal set. Let $U = \{1, 2, 3, 4, 5\}$. Then:

Step 5: Symmetric Difference — combine the two differences:

A common slip …