Mathematics
Equivalence relation
Practice questions
On (A={1,2,3,4}), what are the equivalence classes of the identity relation (I={(1,1),(2,2),(3,3),(4,4)})?On integers, (aRb) holds when (a) and (b) are both positive or both not positive. What type of relation is it?In the previous relation on integers where two integers are related if both are positive or both are not positive, which is the equivalence class of (0)?Which option has all three properties: reflexive, symmetric, and transitive?On real numbers, (aRb) holds when (\lfloor a\rfloor=\lfloor b\rfloor). What type of relation is it?For the relation (\lfloor a\rfloor=\lfloor b\rfloor) on real numbers, which is the equivalence class of (2.7)?On (A={1,2,3,4,5,6}), (aRb) holds when (a) and (b) are both prime or both not prime. What is the equivalence class of (4)?If the classes of an equivalence relation on a set are ({1,2}), ({3,4,5}), and ({6}), what is true about ((2,5))?On the set of non-zero polynomials, (pRq) holds when (p) and (q) have the same degree. Which is the equivalence class of (x^2+1)?On (A={(1,1),(1,2),(2,1),(2,2)}), (aRb) holds when the two ordered pairs have the same first component. Which is the equivalence class of ((1,2))?On integers, (aRb) holds when (a-b) is divisible by (9). Which is the equivalence class of (25)?On (A={1,2,3,4,5,6,7,8}), (aRb) holds when (a\equiv b \pmod{4}). Which is the equivalence class of (7)?On (A={0,1,2,3,4,5}), (aRb) holds when (a) and (b) have the same quotient on division by (3). Which is the equivalence class of (4)?On (A={1,2,3,4,5}), what are the equivalence classes of (R={(1,1),(2,2),(3,3),(4,4),(5,5),(1,3),(3,1),(3,5),(5,3),(1,5),(5,1)})?On (A={1,2,3}), in (R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)}), which pair is necessary for transitivity?On (A={1,2,3,4}), why is (R={(1,1),(2,2),(4,4),(1,2),(2,1)}) not an equivalence relation?If an equivalence relation partitions a set into ({2,4,6},{1,3},{5}), which is the equivalence class of (3)?If an equivalence relation has class sizes (4) and (2), how many ordered pairs are in the relation?Which option gives a valid partition of (A={1,2,3,4,5,6})?Which option does not form a partition of (A={1,2,3,4,5})?