Mathematics
Equivalence relation
Practice questions
On (A={1,2,3,4}), (aRb) holds when (a=b) or (a+b=5). Is this an equivalence relation?On non-zero real numbers, (aRb) holds when (\frac{a}{b}>0). What type of relation is it?For the relation (\frac{a}{b}>0) on non-zero real numbers, what is the equivalence class of (-5)?If an equivalence relation has equivalence classes ({a,b,c}) and ({d,e}), how many ordered pairs are in the relation?How many ordered pairs are in the equivalence relation on (A={1,2,3,4,5}) corresponding to the partition ({1,2},{3},{4,5})?Which option is not a valid partition for an equivalence relation on (A={1,2,3})?On real numbers, (aRb) holds when (a-b) is rational. What type of relation is it?For the relation on real numbers where (a-b) is rational, which element is definitely in the same equivalence class as (\sqrt{2})?Which relation is reflexive but generally not symmetric?On (A={1,2,3,4}), (aRb) holds when (a+b) is even. Which pair belongs to (R)?If (R) is an equivalence relation and ([a]\cap[b]\neq\varnothing), which conclusion is correct?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)?If (A) has (n) elements, how many equivalence classes are formed by the identity relation?If (A) has (n) elements, how many equivalence classes are formed by the universal relation (A\times A)?For the partition ({1,4},{2},{3}) of (A={1,2,3,4}), which pair is not in the corresponding equivalence relation?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?On integers, (aRb) is defined when (a-b) is divisible by (6). Which is the equivalence class of (20)?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)?An equivalence relation on (A={a,b,c,d}) has classes ({a,c}) and ({b,d}). How many ordered pairs are in this relation?If an equivalence relation (R) satisfies ([x]\cap[y]\neq\varnothing), which conclusion is correct?