Today is our topic of discussion Difference of Sets .
Difference of Sets
If A and B are sets, A\ B is {x: x Є A and x∈ B}.
A \ B is called A delete B and the elements of A that are present in B are discarded from A to form A\B. A\B ⊆A.
Complementary Set
If U is an universal set and A ⊆ U, then the complementary set of A is U\A.
So, U\ A = {x: x Є U and x ⊄ A}.
If the elements of A is discarded from the universal set, then we get the complementary set of A and it will be expressed as A’ or Ac.
Power Set
The set of all subsets of A is called the power set of A and it is expressed as P(A). It is to be noted that Ø ⊄ A. For this reason, is also an element of P(A).
Venn Diagram
Sometimes expressing set related information in diagrams is quite convenient. These diagrams are named Venn diagram after the name of John Venn (1834- 1923). This has been discussed briefly in the Mathematics book.
Union of Sets
If A and B are sets then their union of sets is AUB = {x: x Є A or x Є B}.
So, the set formed by the elements of both A and B is called AU B.
Intersection of Sets
If A and B are sets, their intersection of sets is A ∩ B = {x: x Є A and x € B}. That means, the set formed by all common elements of A and B is called An B.
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