Number of subsets of a set of order three is

a)
3

b)
6

c)
8

d)
9

Correct answer is option 'C'. Can you explain this answer?

Question

Number of subsets of a set of order three isa)3b)6c)8d)9Correct answer is option 'C'. Can you explain this answer?

Answer

A set with 'n' elements in it can have '2n' subsets.

eg: Let us consider a set A = {1,2,3}

The possible subsets are:

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

Where, {} is the empty set.

Number of subset = 2ⁿ

order 3 = 2³⇒ 8

Therefore, the number of subsets is 8.

Answer

No. of subsets of a set = 2^N = 2^3 = 8

N= order or no. of elements in the set

Answer

Number of subsets of a set of order three can be determined by using the concept of combinations.
A set of order three means that it contains three elements. Let's assume the elements of the set are A, B, and C.

To find the number of subsets, we need to consider all possible combinations of these elements.

1. Empty Set:
- The empty set is always a subset of any set, so it is included in the count.

2. Single Element Subsets:
- Each element of the set can form a subset on its own.
- So, we have subsets {A}, {B}, and {C}.

3. Two-Element Subsets:
- We can select two elements from the set in different combinations.
- The possible two-element subsets are {A, B}, {A, C}, and {B, C}.

4. Three-Element Subset:
- We can select all three elements of the set as a subset.
- The only three-element subset is {A, B, C}.

Therefore, the total number of subsets is obtained by summing up the subsets from each category:

1 + 3 + 3 + 1 = 8

Hence, the correct answer is option C, 8.

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