Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • The maximum number of equivalence relations on the set A = {1, 2, 3} are (A) 1 (B) 2 (C) 3 (D) 5

The maximum number of equivalence relations on the set A = {1, 2, 3} are

(A) 1 (B) 2

(C) 3 (D) 5

Answers (1)

(D) 5

Given, set A = \{ 1, 2, 3 \} \\

Now, the number of equivalence relations as follows

\\R1 = \{ (1, 1), (2, 2), (3, 3) \} \\ R2 = \{ (1, 1), (2, 2), (3, 3), (1, 2), (2, 1) \} \\ R3 = \{ (1, 1), (2, 2), (3, 3), (1, 3), (3, 1) \} \\ R4 = \{ (1, 1), (2, 2), (3, 3), (2, 3), (3, 2) \} \\ R5 = \{ (1, 2, 3) \Leftrightarrow A \times A = A^2 \} \\

Thus, the maximum number of equivalence relations is ‘5’.

Posted by

infoexpert22

View full answer

Similar Questions

Latest Question