Introduction
Category : JEE Main & Advanced
A set is well defined class or collection of objects.
A set is often described in the following two ways.
(1) Roster method or Listing method : In this method a set is described by listing elements, separated by commas, within braces \[\{\,\}\]. The set of vowels of English alphabet may be described as \[\{a,\,\,e,\,\,i,\,\,o,\,\,u\}\].
(2) Set-builder method or Rule method : In this method, a set is described by a characterizing property \[P(x)\] of its elements \[x\]. In such a case the set is described by \[\{x:P(x)\,holds\}\] or \[\{x|P(x)\,holds\},\] which is read as ‘the set of all \[x\] such that \[P(x)\] holds’. The symbol \['|'\] or \[';'\] is read as ‘such that’.
The set \[A=\{0,\,1,\,4,\,9,\,16,....\}\] can be written as \[A=\{{{x}^{2}}|x\in Z\}\].
| Symbol | Meaning |
| \[\Rightarrow \] | Implies |
| \[\in \] | Belongs to |
| \[A\subset B\] | A is a subset of B |
| \[\Leftrightarrow \] | Implies and is implied by |
| \[\notin \] | Does not belong to |
| s.t.(: or |) \[\forall \] | Such that For every |
| \[\exists \] | There exists |
| iff | If and only if |
| & | And |
| \[a|b\] | a is a divisor of b |
| N | Set of natural numbers |
| I or Z | Set of integers |
| R | Set of real numbers |
| C | Set of complex numbers |
| Q | Set of rational numbers |
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