Sets | Class 11 Mathematics Notes

1.2 Sets and their Representations

In everyday life, collections of objects such as a pack of cards or a cricket team are familiar. In mathematics, sets are similar collections but must be well-defined, meaning it is possible to determine definitively whether an object belongs to the set or not. Examples include odd natural numbers less than 10, vowels in the English alphabet, prime factors of a number, or solutions to an equation. Special sets like natural numbers (N), integers (Z), rational numbers (Q), and real numbers (R) are frequently used. Sets are denoted by capital letters (A, B, C, etc.), and their elements by small letters (a, b, c, x, y, z). The membership of an element in a set is denoted by the symbol ∈, and non-membership by ∉. Sets can be represented in two main ways: roster (tabular) form and set-builder form. In roster form, all elements are listed within curly braces, separated by commas. In set-builder form, a property common to all elements is used to define the set, written as {x : property of x}. This section includes examples illustrating these representations and explains that order and repetition of elements in roster form are immaterial.

🔗 Connection: This section prepares the student to understand the concept of empty sets and classification of sets in the next section.