Subset of a setThis lesson will explain what a subset of a set. We will start with a definition Set B is a subset of a set A if and only if every object of B is also an object of A. We write B Í A By definition, the empty set( { } or Æ ) is a subset of every set Now, take a look at the following Venn diagrams. Definition of Venn Diagrams: Venn Diagrams are closed circles, named after English logician Robert Venn, used to represent relationships between sets B = { a, b, c} A = { a, b, c, f} U = { a, b, c, f} Since all elements of B belong to A, B is a subset of A Proper subset: Set B is a proper subset of set A, if there exists an element in A that does not belong to B. we write B Ì A Having said that, B is a proper subset of A because f is in A, but not in B. We write B Ì A instead of B Í A Universal set: The set that contains all elements being discussed In our example, U, made with a big rectangle, is the universal set Set A is not a proper subset of U because all elements of U are in subset A Notice that B can still be a subset of A even if the circle used to represent set B was not inside the circle used to represent A. This is illustrated below: As you can see, B is still a subset of A because all its objects or elements (c, and d) are also objects or elements of A. B is again a proper subset because there are elements of A that does not belong to B A and B are also subsets of the universal set U, but especially proper subsets since there are elements in U that does not belong to A and B In general, it is better to represent the figure above as show below to avoid being redundant: The area where elements c, and d are located is the intersection of A and B. More on this on a different lesson! If you have any questions about the subset of a set, I will be more than happy to answer them. 




Are you a fan of this site? Support us Our awards! Our partners About me Disclaimer Build your website! Advertise on my site Try our free toolbar Like us on Facebook Take our survey 