Solving Solution Set

Introduction:

Information, lettering, any other article restricted in a set. Example, the solving solution elements of the set {p, q, r} are the letters p, q, and r.

These are used to solving the set problems.

Type 1: Empty set

Type 2: Equivalent sets

Type 3: Singleton set

Type 4: Universal Set

Type 5: Subset

Type 6: Proper Subset

Type 7: Power Set

We are leaving to learn in feature about the laws of set operations, Relations and Functions.


Examples:


1. Identify finite and infinite sets from the following in solving solution set:

(i) {All schools in Tamil Nadu}.

(ii) N.

(iii) The set of all prime numbers.

Solution:

(i) Every part of schools in Tamil Nadu can be counted one by one and we come to an end in the solution counting process. So the set {All schools in Tamil Nadu} is a finite set.

(ii) N = {1, 2, 3,…}. at what time we count up rudiments of N one by one as 1 for 1, 2 for 2, 3 for 3, 4 for 4, we are not able

to come to an end in the counting process. ? the set N is an infinite set.

(iii) When we write the prime numbers one by one as 2, 3, 5, 7, 11, 13, 17 and so on, we are unable to come to an

end in the counting process. ? the set of all solving prime numbers are an infinite set.

Understanding Calculating Percentages is always challenging for me but thanks to all math help websites to help me out.

More Problems:

Represent the following solving sets in Rule Form:


(i) The set of all natural numbers less than 6.


(ii) The set of vowels in English alphabet.


(iii) The set of the numbers 2, 4, 6, … .


Solution: (i) A natural number less than 6 can be described by the statement’s ? N, x < 6.

?the set is { x | x ? N, x < 6}.


(ii) A vowel in English alphabets can be described by the statement: x is a vowel in English alphabet.


? the set is {x | x is a vowel in English alphabet}.


(iii) A number x of the form 2, 4, 6, … can be described by the statement:x = 2n,n ? N.

? the set is { x | x = 2n, n ? N}.

Introduction to subset and proper subset

Introduction to subset and proper subset:

SET:  A set is a collection of distinct objects, considered as an object in its own right.

Example:   A = { 4,9,6,9 } , B = {blue, green , red}

SUBSET:

In mathematics, especially in set theory, a set A is a subset of a set B if A is "contained" inside B. A and B may coincide. The relationship of one set being a subset of another is called inclusion or sometimes containment.

Example : A = { 1,5,3,8,}    , B = { 3,5} ,Here B is subset of A.  That is B `sube`

Proper Subset:

If  A and B are two sets means, A contains all the elements of  B and some additional elements that are not in B.

Example : A = { 3,5,8,10} and B ={ 3,5} .Here B is proper subset of A.

An empty set is always a proper subset of all sets.That is empty set {} is always a proper subset.

This can be denoted as ,  `O/` `subs`

Problems on Subset and Proper Subset :

Problem 1: Find the possible subsets of the set  A = { green ,Yellow,Blue }

Solution:

Given A = { green,yellow,Blue,Black}

We know that empty set is subset of every set.

So subsets of a given set are ,

B = {}

C = {Green,yellow,Blue}

D = { Green,yellow}

E=  { Yellow,Blue}

F = {Green, Blue}

G= {Green}

H = { yellow }

I = {Blue}

The above sets are the subsets of the given set A.

Problem 2 : Find the parent set of the following subsets

B = { 3,8} ,C = { 15,7}, D = { 34,15,8} , E = { 3,7,8}

Solution:

Given B = { 3,8} ,C = { 15,7}, D = { 34,15,8} , E = { 3,7,8}

We know that Subsets are the sets that contains some elements of the Parent set.

So The parent set  might be A = { 3,8,15,7,34,7 }

Problem 3: Express the following sets in-terms of  Venn diagram.

A = { -6 ,8 ,9,0 ,2 } , B = { 0,2,6} , C = { 2,6 } and D = { 34,67,89 }

Solution:

Given A = { -6 ,8 ,9,0 ,2 } , B = { 0,2,- 6} , C = { 2,-6 } and D = { 34,67,89 }

Venn diagram: