C. Calculate the number of proper subset of the following:

Note:

- 2ⁿ is the formula for calculating the number of proper subsets.

- n  will be replaced with the number of elements a set has.

a. X = {A,B,C,}

Answer: 8 proper subsets

Solution:

- 2ⁿ

- Number of elements the set has? {A, B, C} = 3

- 2ⁿ = 2³

- 2³ or 2 × 2 × 2 = 8 proper subsets

b. Y = {x/x is consonant letter in the alphabet)

Answer: 2,097,152 proper subsets

Solution:

- 2ⁿ

- Number of elements the set has? {x/x is consonant letter in the alphabet)

 = 21

- 2ⁿ = 2²¹

= 2²¹ or 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2  

 ×2 × 2 = 2,097,152 proper subsets

c. Z= { }​

Answer: 2 proper subsets

Solution:

- 2ⁿ

- Number of elements the set has? {  }​ = 1

- 2ⁿ = 2¹

= 2¹ or 2 × 1  = 2 proper subsets