Consider the following equivalence relation on the power set Part 2 of 2 - Equiv

Question

Consider the following equivalence relation on the power set Part 2 of 2 - Equivalence Relations Question 2 of 2 1.0 Points Consider the following equivalence relation on the power set of the set S (1,2,3,4). A~B 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. 12) and (3) are in the same equivalence class. B. The equivalence classes of 1,21 and 12,3) are disjoint. c. There are 4 equivalence classes. D. The equivalence class of the empty set contains only itself. Previous Next Save Exit Submit for Grading

Explanation / Answer

S = {1,2,3,4}

A. Since {2} and {3} have same number of elements, any set that has the same number of elements as {2} will also have the same number of elements as {3} and vice versa.

Thus they are in the same equivalence class.

This statement is true.

B. Since {1,2} and {2,3} have same number of elements, they will be in the same equivalence class.

This statement is false.

C. The equivalence class is based on number of elements. Since S has 4 elements, the power set of S has elements that are sets with 0,1,2,3 and 4 elements.

Thus there are 5 equivalence classes.

This statement is false.

D. Since the only set with 0 elements is the empty set,

this statement is true.

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.