Consider the following equivalence relation on the power set of the set S={1,2,3

ID: 3144943 • Letter: C

Question

Consider the following equivalence relation on the power set of the set S={1,2,3,4}.

if and only if A and B have the same number of elements.

Which of the following is true:

Note: You may select more than one.

{2} and {3} are in the same equivalence class.

The equivalence class of the empty set contains only itself.

There are 4 equivalence classes.

The equivalence classes of {1,2} and {2,3} are disjoint.

{2} and {3} are in the same equivalence class.

The equivalence class of the empty set contains only itself.

There are 4 equivalence classes.

The equivalence classes of {1,2} and {2,3} are disjoint.

Lets check option by option

Option A. {2} ~ {3} so each have one element so yes they are same equivalence class. Option A is correct.

Option B. Empty set {} doesn't have any equivalence class. It is itself an empty set. so option B is incorrect.

Option C. Number of equivalence classes where there are 0,1,2,3 and 4 elements are in the set. so there are 5 equivalence classes not 4.

Option D - as both equivalence classes {1,2} and {2,3} have 2 in common than these are not disjoint.

So only option A is correct.

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