Unit 7 What was the condition of the parents of the sick girl on the arrival of the doctor? What was the behavior of Mathilda with the doctor?
Cantor introduced the concept of sets. He had defined a set as a collection of definite and distinguishable objects selected by the means of certain rules or description. Set theory forms the basis of several other fields of study like counting theory, relations, graph theory and finite state machines.
In this chapter, we will cover the different aspects of Set Theory.
Set — Definition A set is an unordered collection of different elements a set is a Well define Collection of objects. A set can be written explicitly by listing its elements using set bracket.
If the order of the elements is changed or any element of a set is repeated, it does not make any changes in the set. The elements are enclosed within braces and separated by commas. The number is also referred as the cardinal number.
It occurs when the number of elements in X is exactly equal to the number of elements in Y. It occurs when number of elements in X is less than or equal to that of Y. It occurs when number of elements in X is less than that of Y. The sets X and Y are commonly referred as equivalent sets.
Types of Sets Sets can be classified into many types.
Some of which are finite, infinite, subset, universal, proper, singleton set, etc. Finite Set A set which contains a definite number of elements is called a finite set. Here set Y is a subset of set X as all the elements of set Y is in set X.
Universal Set It is a collection of all elements in a particular context or application.
All the sets in that context or application are essentially subsets of this universal set. Universal sets are represented as U. In this case, set of all mammals is a subset of U, set of all fishes is a subset of U, set of all insects is a subset of U, and so on.
Empty Set or Null Set An empty set contains no elements. As the number of elements in an empty set is finite, empty set is a finite set. The cardinality of empty set or null set is zero. Equivalent Set If the cardinalities of two sets are same, they are called equivalent sets.
Disjoint Set Two sets A and B are called disjoint sets if they do not have even one element in common.
Venn Diagrams Venn diagram, invented in by John Venn, is a schematic diagram that shows all possible logical relations between different mathematical sets.
The cardinality of a power set of a set S of cardinality n is 2n. Power set is denoted as P S.AP/TS Intermediate Guess Papers Download 1st / 2nd Year With Answers.
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