Which of the following statements are true about an equivalence relation R on a set A? (Select all that apply.) O For all elements a and b in A, if [a]R U [b]R # Ø, then [a]R # [b]R. O For all elements a and b in A, if [a]R N [b]R # Ø, then [a]R = [b]R- O For all elements a and b in A, if [a]R U [b]R # Ø, then [a]R = [b]R- O For all elements a and b in A, if [a]R N [b]R # Ø, then a R b. O For all elements a and b in A, if a R b, then [a]R U [b]R = A.

Which of the following statements are true about an equivalence relation R on a set A? (Select all that apply.) O For all elements a and b in A, if [a]R U [b]R # Ø, then [a]R # [b]R. O For all elements a and b in A, if [a]R N [b]R # Ø, then [a]R = [b]R- O For all elements a and b in A, if [a]R U [b]R # Ø, then [a]R = [b]R- O For all elements a and b in A, if [a]R N [b]R # Ø, then a R b. O For all elements a and b in A, if a R b, then [a]R U [b]R = A.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 6TFE: Label each of the following statements as either true or false. Let R be a relation on a nonempty...

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