Need help Please write clearly Define the set X a b c d e f

Need help! Please write clearly~

Define the set X = {a. b, c, d, e, f}. We will define a relation on the power set of X. denoted P(X) (see the supplementary document if you don\'t know what that is). We will say that for A elementof P(X) and B elementof P(X), that A ~ B is defined to hold true, whenever A and B have the same number of elements (or |A| = |B|). list all of the elements in [{c}]. list all of the elements in [X]. how many elements are in [{c, f}]? how many distinct equivalence classes are there for ~ over P(X)?

Solution

1.[{c}] is set of all subsets of X which contain only one element

So, all element in [{c}] are

{{a},{b},{c},{d},{e},{f}}

2. all elements in [X] are subset of X which contain |X| elements

So only X belongs to [X]

3.

This equivalence class contains all subsets with two elements

Number of such subsets is:C(6,2)=6*5/2=15

4.

Number of elements can vary from 0(empty set) to 6(for X)

So 7 equivalence classes