Question

Be able to state, using set listing notation, different sets of numbers.

Answer 1

Answer:

Set notation is given by

${\bf X}= \{{\bf setofallelements\}}$

Step-by-step explanation:

A set  is a collection of things. The objects in the set are called the elements, and they are expressed within  in  curly braces.

Let X be the set and is notated by

ie, $X=\{set of all elements\}$

For example  if  we list the elements of "the set of things on my alphabets , the set can be in the form

$\{ a,b,c,...,z\}$

Sets are usually notated using capital letters. So let the  set be "A". Then we have:  

$A = \{a,b,c,...,z \}$

If the sets are unordered, which means that the elements in the set have not to be listed in order. The set above mentioned can be easily  written as:

$A = \{ a,c u,d,...,i \}$

To say that any element is an element of a set. . For example, to say that "d is an element of the set A", we would write the following:

d ∈A

This is pronounced as "d is an element of A".

There are the symbols to use:

N : the set of all natural numbers ,Z : the set of all integers

,Q : the set of all rationals ,R : the set of all real numbers.

Sets can be related to each other. If one set contains another set  is called a subset.

Suppose $A=\{ 1, 2, 3 \}$ and

$B = \{ 1, 3, 4, 6 \}$. Then A is a subset of B, since everything in A is also in B. Therfore it can be written as:

A ⊂B

it is pronounced as "is a subset of"or A contains B

To show something is not a subset   

B is not a subset of A  ie, B⊄A  and is pronounced as "B is not a subset of A" or B not contains A

Combination of two sets  is called the union  sets, and is notated by a large U-type symbol. If we only taking common elements from two sets, then it is called the intersection  sets, and is notated  by upside-down U-type symbol. So if

$C = \{ 1, 2, 3, 4, 5, 6 \}$ and $D = \{ 4, 5, 6, 7, 8, 9 \}$, then:

C \cup D =\, ${C \bigcup D}= \{ 1, 2, 3, 4, 5, 6, 7, 8, 9 \}$  

C \cap D = \, ${C \bigcap D}= \{ 4, 5, 6 \}$

These are pronounced as "C union D equals..." and "C intersect D equals...", respectively.