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.

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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}.