Mathematics
Equivalence relation
Practice questions
On non-zero rational numbers, (aRb) holds when (\frac{a}{b}>0). Which is the equivalence class of (-\frac{3}{5})?On real numbers, (aRb) holds when (a-b) is an integer. Which element belongs to the equivalence class of (2.3)?On integers, (aRb) holds when (\lfloor \frac{a}{3}\rfloor=\lfloor \frac{b}{3}\rfloor). Which is the equivalence class of (5)?On natural numbers, (aRb) holds when (a) and (b) have the same last digit. Which is the equivalence class of (42)?On non-zero real numbers, (aRb) holds when (\frac{1}{a}) and (\frac{1}{b}) have the same sign. What type of relation is it?On (A={(1,1),(1,2),(2,1),(2,2),(3,2)}), (aRb) holds when the two ordered pairs have the same second component. Which is the equivalence class of ((1,2))?For points in the plane, (P R Q) holds when (P) and (Q) have the same (y)-coordinate. What is the equivalence class of ((3,5))?On real numbers, (aRb) holds when (|a-2|=|b-2|). What type of relation is it?For the relation (|a-2|=|b-2|) on real numbers, which is the equivalence class of (5)?On natural numbers, (aRb) holds when (a) and (b) have the same sum of digits. What type of relation is it?For the relation based on equal sum of digits, the equivalence class of (23) will be the set of which type of numbers?Which option is not an equivalence relation?On integers, (aRb) holds when (a^2-b^2) is divisible by (3). What type of relation is it?For the relation on integers where (a^2-b^2) is divisible by (3), which element must belong to the class of (2)?If (R) is an equivalence relation and ([a]\neq[b]), which statement is correct?If ([x]={1,4,7}) in an equivalence relation, which of the following pairs is definitely in the relation?Which option gives a relation that is reflexive and symmetric but not necessarily transitive?On (A={1,2,3,4,5,6,7}), (aRb) holds when (a) and (b) are both greater than (4) or both not greater than (4). What is the equivalence class of (6)?On (A={1,2,3,4,5,6}), (aRb) holds when (a) and (b) are both prime or both not prime. Which is the equivalence class of (1)?On (A={1,2,3,4}), (aRb) holds when (a=b) or (a+b=5). How many ordered pairs are in the relation?