Let $A = \{1, 2, 3, 4\}$. Let $R$ be the equivalence relation on $A \times A$ defined by $(a, b)R(c, d)$ if $a + d = b + c$. Find the equivalence class $[(1, 3)]$.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $\{(1, 3), (2, 4)\}$ ##
$[(1, 3)] = \{(x, y) \in A \times A : x + 3 = y + 1\}$
$= \{(x, y) \in A \times A : y - x = 2\} = \{(1, 3), (2, 4)\}$