Sets and Basic Operations on Sets Notation A set will usually be denoted by a capital letter, such as, A,B,X, Y,..., whereas lower-case letters, a, b,

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Sets and Basic Operations on Sets Notation A set will usually be denoted by a capital letter, such as, A,B,X, Y,..., whereas lower-case letters, a, b, c, x, y, z,... will usually be used to denote elements of sets. For example, A = {a, e, i, o u} The second way is to state those properties B = {x : x is an even integer, x > O} which reads: "B is the set of x such that x is an even integer and x > 0"

The statement "p is an element of A" or, equivalently, the statement "p belongs to A" is written p A We also write a, b A to state that both a and b belong to A. The statement that p is not an element of A, that is, the negation of p A, is written p A ∈ ∈ ∈

The union of two sets A and B, denoted by A U B, is the set of all elements which belong to A or B; that is, The intersection of two sets A and B, denoted by A n B, is the set of all elements which belong to both A and B; that is,

Complement The absolute complement, or, simply, complement of a set A, denoted by A C, is the set of elements which belong to U but which do not belong to A; that is, Difference Let A and B be sets. The relative complement of B with respect to A or, simply, the difference of A and B, denoted by A\B, is the set of elements which belong to A but which do not belong to B; that is,

Symmetric Difference The symmetric difference of the sets A and B, denoted by, consists of those elements which belong to A or B but not to both A and B. That is,

1.1. Which of these sets are equal: {r, t, s}, {s, t, r, s}, {t, s, t, r}, {s, r, s, t}? Student Assignment 1.2. List the elements of the following sets where P = {I, 2, 3,...}. (a) A = {x : x P, 3 < x < 12} (b) B = {x : x P, x is even, x < 15} (c) C = {x : x P, 4 + x = 3} (d) D = {x : x P, x is a multiple of 5}. ∈ ∈ ∈ ∈