Question

Write the subset and number of subsets of the following sets.
a) C = {3, 5, 7}
b) F = {}

Answer 1

Answer:

Write the subset and number of subsets of the following sets.

a) C = {3, 5, 7}

b) F = {}If A {1, 3, 5}, then write all the possible subsets of A. Find their numbers.

Solution:

The subset of A containing no elements - { }

The subset of A containing one element each - {1} {3} {5}

The subset of A containing two elements each - {1, 3} {1, 5} {3, 5}

The subset of A containing three elements - {1, 3, 5)

Therefore, all possible subsets of A are { }, {1}, {3}, {5}, {1, 3}, {3, 5}, {1, 3, 5}

Therefore, number of all possible subsets of A is 8 which is equal 23.

Proper subsets are = { }, {1}, {3}, {5}, {1, 3}, {3, 5}

Number of proper subsets are 7 = 8 - 1 = 23 - 1

2. If the number of elements in a set is 2, find the number of subsets and proper subsets.

Solution:

Number of elements in a set = 2

Then, number of subsets = 22 = 4

Also, the number of proper subsets = 22 - 1

= 4 – 1 = 3

3. If A = {1, 2, 3, 4, 5}

then the number of proper subsets = 25 - 1

= 32 - 1 = 31 {Take [2n - 1]}

and power set of A = 25 = 32 {Take [2n]}