Set Builder notation mat

Introduction to the set-Builder notation in mathematics:

In set theory and its applications to mathematics, logic and computer science engineering notation (sometimes simply notation) is a mathematical notation for describing a set of properties, saying that its members must meet. In mathematics, a set in this way is also known as a set of abstract understanding, or as a definition of a set of saturation. (Source: Wikipedia).

Explanation the builder notation in mathematics:

Public property st should be such that it should indicate the objects lay only. For example let's take lay {6, 36, 216}.

Elements 6th, 36, and 216. These rooms have a common property, that they are authority 6. Therefore, the condition x = 6n, where n = 1, 2 and 3 rooms 6, yields 36 and 216. Not another number can be obtained from this condition.

Thus we see that the set {6, 36, 216} represents a collection of all numbers x such that x = 6n, where n = 1, 2, 3. This fact is recorded in the form of {x | x = 6n, n = 1, 2, 3}. In a nutshell, we read it as lying, consisting of all x such that x = 6n, where n = 1, 2, 3.

Here also, the curly braces {} are used to mean ' a '. Vertical bar ' | ' within the parentheses used to mean "what". Common property ' x = 6n, where n = 1, 2 and 3 works as a Builder to lay there and therefore it is in the form of set Builder or rule.

If P is a common joint property, overcome, every object of this st B and in addition to these objects do not object has the property P, then st B is {x | x has property P} and we say that all elements of B that x x has property p.

Problems in set-Builder notation:

Example problem 1:

Represent the builder notation as follows:

((i) the set of all natural numbers less than 8.

(ii) a set of numbers 2, 4, 6, ...

Solution:

(i) natural number is less than 8 can be described by the statement:

x? N, x< 8.="">

So is lying {x | x? N, x< 8}.="">

((ii) number of x in the form of 2, 4, 6, ... can be described in the application:

x = 2n, n? N.

So is lying {x | x = 2n, n? N}.

Example problem 2:

Find lying all even numbers less than 28, express it in the notation lying builder.

Solution:

Put all the even number less than 28.

The number is x = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26}

{x | x is an even number, x< 28}.="">