1.10

MTH-4109-1 Sets, Relations and Functions

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g) G = {..., –3, –2, –1, 0, 1, 2, 3, ...}

.......................................................................................................................

h) H = {0, 2, 4, ..., 94, 96, 98}

.......................................................................................................................

3. Our typographer had a bad day and made a few mistakes listing the elements

of certain sets. Correct the errors.

a) A = {1 2 3 4 5} ...................................................................

b) B = {8, 8, 9, 10, 11, 11, 12} ...................................................................

c) c = {13, 14, 15, 16, 17, ...} ...................................................................

d) D = 1, 3, 5, 7, 9, 11 ...................................................................

We will know that a set is clearly defined if we can determine whether or not any

given element belongs to that set.

To indicate that any element belongs to a set, we use the symbol for

membership, which is denoted by ∈. For instance, the expression x ∈ C means

that element x is part of set C, that it is an element of set C or that it belongs to

set C.

We know that the element 4 belongs to the set of even natural numbers

P = {0, 2, 4, 6, 8, ...}. Hence, we can write 4 ∈ P.

To indicate that an element x belongs to a given set A, we

write x ∈ A.

x ∈ A means "x is an element of set A"

or

"x belongs to set A."