Question

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

Please help ASAP I don't understand this question at all!! :(

Answer 1

Set notation is given by

`{\bf X}= \{{\bf setofallelements\}}`

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.