`\color{green} ✍️` A set is well-defined if
There is no ambiguity as to whether or not an object belongs to it, i.e we can always tell what is and what is not a member of the set.
`\color{green} ✍️` If `color{green} (a \ \ "is an element of a set A"),` we say that `"“ a belongs to A”."` Thus, we write `a ∈ A`.
`\color{green} ✍️` (i) If same element comes twice or more time in set, then it is consider only once at final set.
(ii) Sets are usually denoted by capital letters `A, B, C, X, Y, Z`, etc.
(iii) The elements of a set are represented by small letters `a, b, c, x, y, z`, etc.
`\color{green} ✍️` It may be noted that while writing the set in roster form an element is not generally repeated, i.e., all the elements are taken as distinct.
`\color{green} ✍️` It is not possible to write all the elements of an infinite set within braces `{ }` because the numbers of elements of such a set is not finite.
So, we represent some infinite set in the roster form by writing a few elements which clearly indicate the structure of the set followed ( or preceded ) by three dots.
`\color{green} ✍️` A set does not change if one or more elements of the set are repeated.
`\color{green} ✍️` Every set A is a subset of itself, i.e., `A subset A`.
`\color{green} ✍️` Since the empty set `φ` has no elements, we agree to say that `φ` is a subset of every set.
`\color{green} ✍️` `(a,b]` is also written as ` ]a,b]`
`\color{green}✍️` The number `(b – a)` is called the length of any of the intervals `(a, b), [a, b], [a, b)` or `(a, b].`
`\color{green}✍️` The sets `A – B, A ∩ B` and `B – A` are mutually disjoint sets, i.e., the intersection of any of these two sets is the null set
`\color{green}✍️` If `A` is a subset of the universal set `U`, then its complement `A′` is also a subset of `U.`
`\color{green} ✍️` A set is well-defined if
There is no ambiguity as to whether or not an object belongs to it, i.e we can always tell what is and what is not a member of the set.
`\color{green} ✍️` If `color{green} (a \ \ "is an element of a set A"),` we say that `"“ a belongs to A”."` Thus, we write `a ∈ A`.
`\color{green} ✍️` (i) If same element comes twice or more time in set, then it is consider only once at final set.
(ii) Sets are usually denoted by capital letters `A, B, C, X, Y, Z`, etc.
(iii) The elements of a set are represented by small letters `a, b, c, x, y, z`, etc.
`\color{green} ✍️` It may be noted that while writing the set in roster form an element is not generally repeated, i.e., all the elements are taken as distinct.
`\color{green} ✍️` It is not possible to write all the elements of an infinite set within braces `{ }` because the numbers of elements of such a set is not finite.
So, we represent some infinite set in the roster form by writing a few elements which clearly indicate the structure of the set followed ( or preceded ) by three dots.
`\color{green} ✍️` A set does not change if one or more elements of the set are repeated.
`\color{green} ✍️` Every set A is a subset of itself, i.e., `A subset A`.
`\color{green} ✍️` Since the empty set `φ` has no elements, we agree to say that `φ` is a subset of every set.
`\color{green} ✍️` `(a,b]` is also written as ` ]a,b]`
`\color{green}✍️` The number `(b – a)` is called the length of any of the intervals `(a, b), [a, b], [a, b)` or `(a, b].`
`\color{green}✍️` The sets `A – B, A ∩ B` and `B – A` are mutually disjoint sets, i.e., the intersection of any of these two sets is the null set
`\color{green}✍️` If `A` is a subset of the universal set `U`, then its complement `A′` is also a subset of `U.`