Question:
Let A = {1, 2, 3}. Then, the number of equivalence relations containing (1, 2) is
(a) 1
(b) 2
(c) 3
(d) 4
Solution:
(b) 2
There are 2 equivalence relations containing {1, 2}.
R = {(1, 2)}
S = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1), (2, 3), (3, 2), (1, 3), (3, 1)}
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