Question

9. The Set of all three digit numbers, sum of whose digits is less than 3

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Answer 1

SET

Let us first understand what is a set.

Set :- A set is a collection of objects or elements. They are denoted by capitalized letters like A,B,E etc.

Sets can be represented in two types :-

1.    Set-Builder Form
2.    Roster Form

Elements of the set are placed between curly braces {}.

Eg.:- Set of natural numbers up to 10. Let us denote it by N.

N = {1,2,3,4,5,6,7,8,9,10}

Now, back to the question.

Let us have a look at those three digit numbers, whose digits when added gives us a sum of less than 3.

The numbers will include 0, 1, and 2.

Let us have a look at the possibilities :-

• Number cannot start with 0 as it has to be a three digit number.
• If it starts with 1, then possible numbers are 100, 101, and 110.
• If it starts with 2, then the possible number is 200.

Numbers are :- 100, 101, 110, 200

So, set will be A = { 100, 101, 110, 200 }

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Answer 2

HELLO DEAR,  What is set?  Set is a collection of objects or elements, they are denoted by the capital letters like A,B,C,X,Y,Z etc.  There are two method of representing the sets. 1. Set- Builder Form 2. Roster Form  GIVEN:- To find the set of three digits number whose digit sum is less than 3.  SOLUTION:- The possibility of numbers that can be included in this three digits number as per question is 0,1,2.  So, the number that can be made of three digits are whose sum is less than 3 are; (100),(101),(110),(200).  I HOPE IT'S HELP YOU DEAR, THANKS.