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  1. Glossary
  2. /Mathematics
  3. /Set

What is Set?

In short

A set is a collection of distinct objects, called elements, written inside curly brackets, for example A={1,2,3}A = \{1, 2, 3\}A={1,2,3}.

In simple words

The order of the elements does not matter, and an element is not repeated. We write 2∈A2 \in A2∈A to say that 222 belongs to AAA. A subset B⊆AB \subseteq AB⊆A has every element of BBB in AAA. The union A∪BA \cup BA∪B has the elements in either set, and the intersection A∩BA \cap BA∩B has the elements in both. The empty set ∅\varnothing∅ has no elements.

Example

Let A={1,2,3,4}A = \{1, 2, 3, 4\}A={1,2,3,4} and B={3,4,5}B = \{3, 4, 5\}B={3,4,5}. Then A∪B={1,2,3,4,5}A \cup B = \{1, 2, 3, 4, 5\}A∪B={1,2,3,4,5} and A∩B={3,4}A \cap B = \{3, 4\}A∩B={3,4}.

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Related terms

  • Ordered Pair
  • Function

← All glossary terms

Practise

  1. Three sets of real numbers are defined by A = {x : |2x - 3| < 7}, B = {x : x² - 9x + 8 ≤…Medium
  2. Let U = {1, 2, …, 12}, A = {2, 4, 6, 8, 10, 12} and B = {3, 6, 9, 12}…Medium
  3. Let A = {a, b, {c, d}}. Say which of these are true…Medium
  4. In a group of 80 students, 46 like football, 38 like cricket and 20 like both…Medium
All problems on this topic →

Quick questions

  1. Let U = {1, 2, 3, 4, 5}. How many ordered pairs (X, Y) are there in which X and Y are…
Hard
  • In a class, 50 students study mathematics, 45 study physics and 40 study chemistry. Of…Medium
  • How many proper subsets does a set of 4 elements have?Medium

    • More Mathematics terms

    1. Algebraic Identity
    2. Arithmetic Progression
    3. Complex Number
    4. Derivative
    5. Isosceles Triangle
    6. Linear Equation
    All Mathematics terms →

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