Question

Let S = {1, 2, 3}. How many subsets does S contain?​

Answer 1

Step-by-step explanation:

the number of subsets of a set having[math] n[/math] elements is [math]2^n[/math]

I will explain it thru ur given set. Your set S contains 3 elements.

we can choose 1 element by 3 ways (1,2 or3)

we can choose 2 elements by 3 ways { (1,2) (2,3) or (3,1) }

we can choose 3 elements using only 1 way {1,2,3} bcoz there are only 3 elements in total

Also {} (empty set) is subset of all sets

So in total we get 3 + 3+ 1 +1 = 8 = [math]2^3[/math]

ex...

Let S = {1,2,3}. How many subsets does S contain?

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the number of subsets of a set having n elements is 2n

I will explain it thru ur given set. Your set S contains 3 elements.

we can choose 1 element by 3 ways (1,2 or3)

we can choose 2 elements by 3 ways { (1,2) (2,3) or (3,1) }

we can choose 3 elements using only 1 way {1,2,3} bcoz there are only 3 elements in total

Also {} (empty set) is subset of all sets

So in total we get 3 + 3+ 1 +1 = 8 = 23

Let N be the number of elements in set S. Then number of subsets in S is 2^N.

Eg:

S={} N=0 2^N= 2^0= 1

subsets={ {} } it contain only empty set .

S={1} N=1 2^N= 2^1= 2

subsets={ {},{1}}

S={1,2} N=2 2^N= 2^2= 4

subsets={ {},{1},{2},{1,2}}

S={1,2,3} N=3 2^N= 2^3= 8

subsets={ {},{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}}

Answer 2

Answer:

Step-by-step explanation:

It contains 8 subsets.

no of subset= $2^{n}$

                     = $2^{3}$

                      =8

Hope it is helpful