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A set contains nine elements.
a) How many subsets does it have?
b) How many proper subsets does it have?
a) The set has _ subsets. (Simplify your answer.)​

Respuesta :

absor201

Answer:

a) The set has 512 subsets.

b) The set has 511 proper subsets.

Step-by-step explanation:

a) The set has 512 subsets.

Reason:

Number of all subsets of a set containing n elements is 2^n subsets,

Then the number of all subsets of a set containing 9 elements is:

2^n=2^9

=2*2*2*2*2*2*2*2*2

=512 subsets.

b) The set has 511 proper subsets.

Reason:

Number of proper subsets of a set containing n elements is 2^n-1 proper subsets,

Then the number of proper subsets of a set containing 9 elements is:

2^n -1 = 2^9 -1

=2*2*2*2*2*2*2*2*2 -1

=512-1

=511 proper subsets....

Eduard22sly

A. The number of subsets present in the set is 512 subsets

B. The number of proper subsets present in the set is 511 proper subsets

A. How to determine the number of subsets

From the question given above, the following data were obtained:

  • Number of element (n) = 9
  • Number of subset =?

The number of subset present in the set can be obtained as follow:

Number of subset = 2ⁿ

Number of subset = 2⁹

Number of subset = 512 subsets

B. How to determine the number of proper subsets

  • Number of element (n) = 9
  • Number of proper subset =?

Number of proper subset = 2ⁿ – 1

Number of proper subset = 2⁹ – 1

Number of proper subset = 512 – 1

Number of proper subset = 511 proper subsets

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