Mathematics
Equivalence relation
Practice questions
Which option gives an equivalence relation?On (A={1,2,3,4,5,6,7,8,9}), (aRb) holds when (a\equiv b \pmod{5}). Which is the equivalence class of (9)?If ([a]={2,5,8}) and the relation is an equivalence relation, which pair must surely belong to the relation?If (R) is an equivalence relation and ((x,y)\in R), which statement must be true?Which relation is transitive but generally not symmetric?On natural numbers, (aRb) holds when (a) and (b) have the same number of digits. What type of relation is it?For the relation on natural numbers based on having the same number of digits, which is the equivalence class of (145)?For lines in a plane, (lRm) holds when (l) and (m) are parallel or identical. What type of relation is it?On (A={1,2,3,4,5,6}), (aRb) holds when (a) and (b) are both less than (4) or both not less than (4). What is the equivalence class of (2)?On (A={1,2,3,4,5}), what are the equivalence classes of (R={(1,1),(2,2),(3,3),(4,4),(5,5),(1,5),(5,1),(2,4),(4,2)})?Which option gives a reflexive relation on (A={1,2,3})?Which option gives a symmetric relation on (A={1,2,3})?Which option gives a transitive relation on (A={1,2,3})?On (A={1,2,3,4}), (aRb) holds when (a=b) or ({a,b}={1,2}). What are the classes of this relation?If (A) has (5) elements and the sizes of the equivalence classes are (2,2,1), how many pairs are in the relation?If (R) is an equivalence relation and ([a]=A), which statement about (a) is correct?If (R) is an equivalence relation, why can ([a]) not be empty?On (A={1,2,3,4,5,6}), (aRb) holds when (a\equiv b \pmod{2}). Which partition is formed by this relation?Which option states a general property of classes formed by an equivalence relation?For (A={1,2,3,4}), let (R=A\times A). How many equivalence classes does this relation have?