introduction to set theory elements

Intersection of two sets A and B is a set whose elements belong to both A and B. ..

If every element of A belongs to a set B, and every element of B belongs to C, then clearly every element of A belongs to C. In other words A B and B C then A C..

If A and B are sets such that each element of A is an element of B, then we say that A is a subset of B and write A B. ..

Venn Diagrams [Euler-Venn Diagrams] - A Venn diagram is a pictorial representation of sets by set of points in the plane. The universal set U is represented pictorially by interior of a rectangle and the other sets are represented by closed figures viz circle..

We must prove two statements. If x A and x B then, by the statement "two sets A and B are different if there exists an element which belongs to one set but not to the other" and by hypothesis, A = B is contradicted. Thus A B. Similarly B A. If A ..

1. The numbers 2, 3, 5 and 8. 2. The solutions of the equation x 2 - 2x - 15 = 0. 3. The letters of the word "Chase". 4. People living in our locality. 5. The students Mary, Hillary, Catherine. 6. The workers who are absent from the factory. 7. The capital cities of Asia. 8. The positive even int..

The statement A B that every element of A is also in the set B, which includes the possibility that A = B. The statement A B (A is a proper subset of B) that A is a subset of B and A B; hence there exists at least one element in B which is not in A. ..

A well-defined collection of distinct objects is called a set..

Sets..

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