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Class 12 · Mathematics
→On real numbers, (aRb) holds when (a^3=b^3). What type of relation is it?
Class 12 · Mathematics
→On integers, (aRb) holds when (a\equiv b \pmod{8}). How many distinct equivalence classes are there?
Class 12 · Mathematics
→If an equivalence relation has classes ({p,q,r}) and ({s}), how many ordered pairs are in the relation?
Class 12 · Mathematics
→On (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,4),(4,1)}) is given. What are its equivalence classes?
Class 12 · Mathematics
→On (A={1,2,3,4,5,6,7}), (aRb) holds when (a) and (b) have the same remainder on division by (3). Which is the equivalence class of (4)?
Class 12 · Mathematics
→On integers, (aRb) holds when (a-b) is divisible by (7). Which is the equivalence class of (15)?
Class 12 · Mathematics
→If an equivalence relation (R) satisfies ([x]\cap[y]\neq\varnothing), which conclusion is correct?
Class 12 · Mathematics
→An equivalence relation on (A={a,b,c,d}) has classes ({a,c}) and ({b,d}). How many ordered pairs are in this relation?
Class 12 · Mathematics
→On (A={1,2,3,4,5,6}), (aRb) holds when (a) and (b) have the same remainder on division by (3). Which of the following pairs is not in (R)?
Class 12 · Mathematics
→On integers, (aRb) is defined when (a-b) is divisible by (6). Which is the equivalence class of (20)?
Class 12 · Mathematics
→On (A={1,2,3,4,5,6}), (aRb) holds when (a) and (b) give the same remainder on division by (3). Which statement is correct?
Class 12 · Mathematics
→For the partition ({1,4},{2},{3}) of (A={1,2,3,4}), which pair is not in the corresponding equivalence relation?
Class 12 · Mathematics
→If (A) has (n) elements, how many equivalence classes are formed by the universal relation (A\times A)?
Class 12 · Mathematics
→If (A) has (n) elements, how many equivalence classes are formed by the identity relation?
Class 12 · Mathematics
→On (A={1,2,3,4,5,6,7,8}), (aRb) holds when (a\equiv b \pmod{4}). What is the equivalence class of (2)?
Class 12 · Mathematics
→If (R) is an equivalence relation and ([a]\cap[b]\neq\varnothing), which conclusion is correct?
Class 12 · Mathematics
→On (A={1,2,3,4}), (aRb) holds when (a+b) is even. Which pair belongs to (R)?
Class 12 · Mathematics
→Which relation is reflexive but generally not symmetric?
Class 12 · Mathematics
→For the relation on real numbers where (a-b) is rational, which element is definitely in the same equivalence class as (\sqrt{2})?
Class 12 · Mathematics
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