One of the important theories in modern mathematics is the set theory. This theory has been present now for a very long time. This was developed during the 1870’s itself. There are various operations in the set theory. Set is basically a collection of objects. When it comes to sets in mathematics, the objects must be related to mathematics. There is the presence of a universal set in set theory. This acts as the reference set. Other sets are compared with the same. Set theory is best explained with the help of Venn diagrams. The operation on sets like union, intersection, and compliment and so on can be well represented with the help of Venn diagrams. The subset R contains some of the elements present in R and not all the elements.’ R’ acts as the universal set in this case. The concepts sets and subsets are closely related. Without the presence of one the other doesn’t exist. The definition of subset is that it is a set which contains some of the elements present in the original set.
An example can be used to explain the concept. A set has elements {x, y, z} and another one contains {x). The latter set is the subset of the former one. There can be a number of subsets of the same set. If there was another set containing the element {y}, then it also becomes the subset of the given set. The subset notation is used to convey that a particular set is the subset of the other set. The other set is called the super set. It contains all the elements present in the subset and the subset contains some of the elements of the super set. This is nothing but the subset is a part of the super set.
Set theory can be very helpful in solving mathematical problems. The Venn diagrams give a clear picture on the sets and their operations. By the Venn diagrams problems can be solved. So, lot of arithmetical calculations can be avoided. The process also becomes very simple and easy to understand. Once one is thorough with the concepts of the set theory, the problems can be very easily solved. One of the important operations in set theory is that of intersection of two sets. The intersection of two sets yields a new set which contains the common elements of both the sets.
An example can be used to explain the concept. A set has elements {x, y, z} and another one contains {x). The latter set is the subset of the former one. There can be a number of subsets of the same set. If there was another set containing the element {y}, then it also becomes the subset of the given set. The subset notation is used to convey that a particular set is the subset of the other set. The other set is called the super set. It contains all the elements present in the subset and the subset contains some of the elements of the super set. This is nothing but the subset is a part of the super set.
Set theory can be very helpful in solving mathematical problems. The Venn diagrams give a clear picture on the sets and their operations. By the Venn diagrams problems can be solved. So, lot of arithmetical calculations can be avoided. The process also becomes very simple and easy to understand. Once one is thorough with the concepts of the set theory, the problems can be very easily solved. One of the important operations in set theory is that of intersection of two sets. The intersection of two sets yields a new set which contains the common elements of both the sets.
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