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Class 12 · Mathematics · Medium
→If (R) is an equivalence relation and ([a]\neq[b]), which statement is correct?
Class 12 · Mathematics · Medium
→For the relation on integers where (a^2-b^2) is divisible by (3), which element must belong to the class of (2)?
Class 12 · Mathematics · Medium
→On integers, (aRb) holds when (a^2-b^2) is divisible by (3). What type of relation is it?
Class 12 · Mathematics · Medium
→Which option is not an equivalence relation?
Class 12 · Mathematics · Medium
→For the relation based on equal sum of digits, the equivalence class of (23) will be the set of which type of numbers?
Class 12 · Mathematics · Medium
→On natural numbers, (aRb) holds when (a) and (b) have the same sum of digits. What type of relation is it?
Class 12 · Mathematics · Medium
→For the relation (|a-2|=|b-2|) on real numbers, which is the equivalence class of (5)?
Class 12 · Mathematics · Medium
→On real numbers, (aRb) holds when (|a-2|=|b-2|). What type of relation is it?
Class 12 · Mathematics · Medium
→For points in the plane, (P R Q) holds when (P) and (Q) have the same (y)-coordinate. What is the equivalence class of ((3,5))?
Class 12 · Mathematics · Medium
→On (A={(1,1),(1,2),(2,1),(2,2),(3,2)}), (aRb) holds when the two ordered pairs have the same second component. Which is the equivalence class of ((1,2))?
Class 12 · Mathematics · Medium
→On non-zero real numbers, (aRb) holds when (\frac{1}{a}) and (\frac{1}{b}) have the same sign. What type of relation is it?
Class 12 · Mathematics · Medium
→On natural numbers, (aRb) holds when (a) and (b) have the same last digit. Which is the equivalence class of (42)?
Class 12 · Mathematics · Medium
→On integers, (aRb) holds when (\lfloor \frac{a}{3}\rfloor=\lfloor \frac{b}{3}\rfloor). Which is the equivalence class of (5)?
Class 12 · Mathematics · Medium
→On real numbers, (aRb) holds when (a-b) is an integer. Which element belongs to the equivalence class of (2.3)?
Class 12 · Mathematics · Medium
→On non-zero rational numbers, (aRb) holds when (\frac{a}{b}>0). Which is the equivalence class of (-\frac{3}{5})?
Class 12 · Mathematics · Medium
→Which option does not form a partition of (A={1,2,3,4,5})?
Class 12 · Mathematics · Medium
→Which option gives a valid partition of (A={1,2,3,4,5,6})?
Class 12 · Mathematics · Medium
→If an equivalence relation has class sizes (4) and (2), how many ordered pairs are in the relation?
Class 12 · Mathematics · Medium
→If an equivalence relation partitions a set into ({2,4,6},{1,3},{5}), which is the equivalence class of (3)?
Class 12 · Mathematics · Medium
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