Let \(A = \{1, 2, 3, 4, 5, 6\}\) and let R be the equivalence relation on \(A \times A\) defined by \((a, b)\,R\,(c, d)\) if \(a + d = b + c\). The equivalence class \([(2, 5)]\) is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\{(1, 4), (2, 5), (3, 6)\}\)
The condition \(a + d = b + c\) can be rewritten as
\(b - a = d - c\)
So (c, d) is in the equivalence class of (2, 5) exactly when
\(d - c = 5 - 2 = 3\)
with both c and d in A. The pairs are
\((1, 4), (2, 5), (3, 6)\)
(c = 4 would need d = 7, which is not in A.) So \([(2, 5)] = \{(1, 4), (2, 5), (3, 6)\}\).