Meaning and Notation of a Set

A set is simply a well-defined collection of distinct objects — well-defined meaning that for any given object we can decide, with total certainty, whether it belongs to the collection or not. "The set of districts in Odisha" is well-defined, since any place-name can be checked against Odisha's official district list; "the set of popular sweet shops in Bhubaneswar" is not, because "popular" has no fixed test everyone agrees on. This distinction is exactly what separates a mathematical set from a casual, everyday grouping.

Sets are generally denoted by capital letters — $A$, $B$, $X$ — and their members (called elements) are written inside curly braces $\{\ \}$. If an object $x$ belongs to a set $A$, we write $x \in A$ (read "$x$ belongs to $A$"); if it does not, we write $x \notin A$.

For instance, if $A = \{5, 10, 15, 20\}$ is the set of multiples of 5 up to 20, then $10 \in A$ but $12 \notin A$. Two sets are called equal when they contain exactly the same elements — the order of listing never matters, so $\{3, 1, 2\}$ and $\{1, 2, 3\}$ are the same set.

Set theory is the language every later topic in this Odisha CHSE Class 11 Business Mathematics and Statistics course is built on top of — probability and functions both rest on the vocabulary introduced here. The syllabus itself is not lifted from any single national board's textbook; the Odisha CHSE Std-11 Business Mathematics & Statistics course draws on the same universal mathematical principles of set theory that every commerce mathematics syllabus in India shares, presented here in Odisha's own treatment and sequence.