A set is a collection of distinct objects, which can be anything from numbers to colors to people. Sets are usually denoted by capital letters, and their elements are enclosed in curly braces. For example, the set of all even numbers can be written as {2, 4, 6, 8, …}, while the set of primary colors can be written as {red, blue, yellow}.
ets can be combined using various operations, such as union, intersection, and complement. The union of two sets A and B is the set of all elements that belong to either A or B (or both), and is denoted by A ? B. The intersection of two sets A and B is the set of all elements that belong to both A and B, and is denoted by A ? B. The complement of a set A is the set of all elements that do not belong to A, and is denoted by A’.
Venn diagrams are a useful tool for visualizing sets and their relationships. A Venn diagram consists of one or more circles, each representing a set, and the area inside the circle represents the elements of the set. The circles can overlap, and the overlapping region represents the elements that belong to both sets. For example, if we have two sets A and B, we can draw a Venn diagram with two circles, one for A and one for B, and the overlapping region represents the elements that belong to both A and B.
Venn diagrams can be used to illustrate various set operations. For example, the union of two sets A and B can be represented by the entire area inside both circles, while the intersection of A and B can be represented by the overlapping region. The complement of a set A can be represented by the area outside the circle representing A.
Introduction To Sets & Venn Diagrams image
