The number of proper subsets of the set { 1 , 2 , 3 } is ___. Options: A . &nbsp8 B . &nbsp7 C . &nbsp6 D . &nbsp5

The number of proper subsets of the set {1,2,3} is __

Question

The number of proper subsets of the set

{1, 2, 3}

is ___.

Options:

A . 8

B . 7

C . 6

D . 5

Answer: Option B
:
B
A set of

n

elements has

2^{n}

subsets.
Every set is a subset of itself.
Thus, the number of proper subsets of a set is

2^{n} - 1

subsets.
The set

{1, 2, 3}

has 3 elements and hence,

2^{3} - 1 = 7

proper subsets.

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