# number of subsets of a set of order three is

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## Number of subsets of a set of order three is:

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Question

## Number of subsets of a set of order three is:

**A**

## 3

**B**

## 6

**C**

## 8

**D**

## 9

Medium

## The number of subsets of a set of order three is a class 9 maths CBSE

The number of subsets of a set of order three is a 3 b 6 c 8 d 9

The number of subsets of a set of order three isa) 3 3 b) 6 6 c) 8 8 d) 9 9 Answer Verified 198k+ views 1 likes

**Hint**: The number of subsets for a set containing ‘n’ number of elements is given by the formula

2 n 2n

. For example consider the set

A={a,b,c,d,e} A={a,b,c,d,e}

, this set contains five elements so the total number of subsets would be

2 5 25 which is equal to 32 32

**Complete step-by-step answer**:

Given to us that the order of a set is three i.e. the number of elements in the set is three.

We are asked to find the number of subsets for this set.

In order to find this, we apply the formula, total number of subsets for a set containing ‘n’ elements is

2 n 2n

In the question given to us, the value of ‘n’ is two.

So the number of subsets for a set with three elements will be

2 3 23

which by solving, we get

8 8

Therefore the total numbers of subsets for the given set with order three is eight.

Therefore the total number of subsets for a set containing three elements are

eight eight i.e. option c.

**So, the correct answer is “Option C”.**

**Note**: We can also explain this by taking an example of a set with three elements as

S={1,2,3} S={1,2,3}

To write the subsets of this set, we start with subsets of single order:

{1},{2},{3} {1},{2},{3}

Subsets of order two:

{1,2},{2,3},{1,3} {1,2},{2,3},{1,3}

We know that every set is a subset of itself and also null set is a subset of every set so the rest of the subsets are

{1,2,3},{∅} {1,2,3},{∅}

By adding all the subsets we get eight. Therefore the total number of subsets would be eight.

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Related Questions Question 1

Decide, among the following sets, which sets are subsets of one and another.

A={x:x∈Randxsatisfy x 2 −8x+12=0} B={2,4,6} C={2,4,6,8,......} D={6}

A={x:x∈Randxsatisfyx2−8x+12=0}B={2,4,6}C={2,4,6,8,......}D={6}

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## What will be The number of proper subsets of a set of order three is?

Answer (1 of 5): The formula for the number of subsets is given by 2^n Where n=order of the sets. Since the order of your set is 3, therefore it has 2^3 = 8 subsets. Out of these, one is the given set itself ,since you want the proper subsets,so you need to exclude it. Hence,the answer you ar...

What will be The number of proper subsets of a set of order three is?

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Sort John O'Donovan

Former Head of Department (Maths) (1978–2005)Author has 102 answers and 69K answer views2y

A proper subset of A is a subset of A but excluding the set A itself. However, it does include the empty set. (unless A = {})

So if A = {a,b,c} the proper subsets are {}, {a}, {b}, {c}, {a,b}, {a,c}, {b,c}. So the answer is 7.

The formula is (2^n) -1. In this case 2^3 -1 = 8 - 1 = 7

Please note that you cannot count {a,b} and {b,a} as distinct subsets.

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How many subsets does the set

F={2,3,4,7,8} F={2,3,4,7,8} have?

Manjunath Subramanya Iyer

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A set having n elements has 2^n subsets including the null set and the whole set.

A proper subset is a subset of A set wherein the main set has at least one element more than the proper set. Hence the main set cannot be the proper subset of itself.

Hence we have 2^n - 1 proper subsets for a set containing n elements.

In the present case of the set having 3 elements, the number of proper subsets is 2³ - 1 = 7.

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What is the difference between a subset and a proper subset? What are their symbols?

Originally Answered: What is the difference between a subset and proper subset?

If every member of one set is also a member of a second set, then the

first set is said to be a subset of the second set. Usually, it turns

out that the first set is smaller than the second, but not always. The

definition of "subset" allows the possibility that the first set is

the same as (equal to) the second set. But a "proper subset" must be

smaller than the second set.

Example 1:

The set {2,3,5,7} is a subset of {2,3,5,7}.

The set {2,3,5,7} is NOT a proper subset of {2,3,5,7}.

The set {2,3,5} is a proper subset of {2,3,5,7}.

Example 2:

It is possible to specify sets in different w

Henk Brozius

Studied MathematicsUpvoted by

Keith Ramsay

, Ph.D. in mathematics and

Terry Moore

, M.Sc. Mathematics, University of Southampton (1968)Author has 2.5K answers and 839.3K answer views1y

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Is an empty set a proper subset of all sets?

Originally Answered: Is an empty set a proper set of all sets?

There is only one empty set.

The empty set is a subset of every set.

The empty set is not a proper subset of the empty set.

The empty set is a proper subset of every non-empty set.

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A={1,2,{3,4}} A={1,2,{3,4}} ? David Joyce

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Suppose that A is a set containing 12 elements. What is the number of different subsets of A?

Far more important than knowing the number of subsets in a set with 12 elements is knowing the general principle which answers this question and the reason why it works.

Theorem. The number of subsets in a set with

n n elements is 2 n . 2n.

Idea of the proof. Order your subset so there’s a first element, second element, and so forth. You can specify a subset by first saying whether the first element is in it. Either it is or it isn’t. That’s 2 choices. Second say whether the second element is in it. That’s 2 choices. Then the third, that’s 2 choices. These choices can be made in any way, that is, they’

Avani Goel 5y Related

What is the number of proper subsets of set {A, B, C, and D}?

Number of proper subsets would be (2^n)-2

Here n=4

So number of proper subsets will be

(2^4)-2 =14

This can be explained as follows

Given set {A, B, C, D}

Now all subsets:{}, {A}, {B}, {C}, {D}, {A, B}, {B, C}, {C, D}, {D, A}, {A, C}, {B, D}, {A, B, C}, {A, B, D}, {A, C, D}, {B, C, D}, {A, B, C, D}

They are totally 16 in number i. e. 2^n

Now the empty set {} and complete set {A, B, C, D} are not considered proper subsets.

Guys, does anyone know the answer?