Mathematics
Equivalence relation
Practice questions
On integers, (aRb) holds when (a+b) is odd. Why is it not an equivalence relation?On (A={-2,-1,0,1,2}), under the relation (|a|=|b|), what is the equivalence class of (2)?For points in a plane, (P R Q) holds when (P) and (Q) have the same (x)-coordinate. What type of relation is this?If an equivalence relation partitions a set into ({1,4},{2,5},{3,6}), what is the equivalence class of (4)?Which option forms a valid partition of (A={1,2,3,4})?If (R) is an equivalence relation on (A) and (aRb), what is true about the equivalence classes of (a) and (b)?On (A={1,2,3,4}), for (R={(1,1),(2,2),(3,3),(4,4),(1,3),(3,1)}), what are the equivalence classes?On natural numbers, (aRb) holds when (a) and (b) have the same last digit. What type of relation is it?For the relation on natural numbers where numbers have the same last digit, what is the equivalence class of (23)?For (A={1,2,3}), which statement is correct about the identity relation (I={(1,1),(2,2),(3,3)})?On integers, (aRb) holds when (a-b) is a multiple of (5). How many distinct equivalence classes are there?Which option definitely gives a relation that is not an equivalence relation?On (A={1,2,3,4,5}), (aRb) holds when (|a-b|) is even. What is the equivalence class of (1)?If (R) is an equivalence relation, what is true about ([a]) for any (a\in A)?On a set of students, (aRb) holds when (a) and (b) study in the same class. What type of relation is it?On (A={1,2,3,4}), the relation (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(1,3),(3,1)}) is not an equivalence relation. Which missing pair shows the failure of transitivity?On integers, (aRb) holds when (a^2=b^2). What type of relation is it?For the relation (a^2=b^2) on integers, what is the equivalence class of (-3)?On (A={1,2,3,4,5,6}), (aRb) holds when (a) and (b) have the same remainder on division by (2). Which pair is not in (R)?Which statement correctly describes equivalence classes?