Respuesta :
Answer:
(a) Total No. of Subsets = 128
(b) Total No. of Proper Subsets = 127
Step-by-step explanation:
First we need to define the set of days of the week.
Set of Days of Week = {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}
It is evident from the set of days of the week, that it contains 7 elements.
(a)
The total no. of subsets of a given set is given by the following formula:
Total No. of Subsets = 2^n
where,
n = no. of elements of the set = 7
Therefore,
Total No. of Subsets = 2^n
Total No. of Subsets = 2^7
Total No. of Subsets = 128
(b)
The total no. of proper subsets of a given set is given by the following formula:
Total No. of Proper Subsets = (2^n) - 1
where,
n = no. of elements of the set = 7
Therefore,
Total No. of Proper Subsets = (2^n) - 1
Total No. of Proper Subsets = (2^7) - 1 = 128 - 1
Total No. of Proper Subsets = 127
The total number of subsets is 128 and the total number of proper subsets is 127 and this can be determined by using the given data.
Given :
The set of days of the week.
The following steps can be used in order to determine the number of subsets and the number of proper subsets:
Step 1 - According to the given data, the set is given below:
S = {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}
Step 2 - Now, the total number of subsets is given by the formula [tex]2^n[/tex] where 'n' is the number of elements of the set.
[tex]{\rm Total\;Subsets} = 2^7\\{\rm Total\;Subsets} = 128[/tex]
Step 3 - Now, the total number of proper subsets is given by the formula [tex](2^n-1)[/tex] where 'n' is the number of elements of the set.
[tex]{\rm Total\; Proper\; Subsets}=2^7-1\\{\rm Total\; Proper\; Subsets}=127[/tex]
a) The total number of subsets is 128.
b) The total number of proper subsets is 127.
For more information, refer to the link given below:
https://brainly.com/question/2094789
