Mathematics
Equivalence relation
Practice questions
Which option gives the identity relation on (A={1,2,3,4})?Which option gives the universal relation on (A={1,2})?If (A) has (6) elements and the universal relation is taken, how many ordered pairs are in the relation?If (A) has (6) elements and the identity relation is taken, how many ordered pairs are in the relation?Which statement correctly describes the connection between an equivalence relation and a partition?When an equivalence relation is formed from a partition, which elements are related?For the partition ({1,6},{2,5},{3,4}) of (A={1,2,3,4,5,6}), which pair belongs to the corresponding equivalence relation?For the same partition ({1,6},{2,5},{3,4}), which pair will not belong to the relation?On integers, (aRb) holds when (a) and (b) are both even or both not even. What type of relation is it?On integers, (aRb) holds when one of (a) and (b) is even and the other is odd. Why is it not an equivalence relation?On (A={1,2,3,4}), (aRb) holds when (a+b) is even. How many ordered pairs are in the relation?On real numbers, (aRb) holds when (a-b) is irrational. Why is it not an equivalence relation?On real numbers, (aRb) holds when (a-b) is rational. Which element belongs to the class of (\sqrt{3})?Which option gives a relation that is not reflexive?Which option gives a relation that is not transitive?On (A={1,2,3,4,5,6}), (aRb) holds when (a\equiv b \pmod{3}). How many pairs are in this relation?If (R) is an equivalence relation and (x\in[y]), which conclusion is correct?If (R) is an equivalence relation, when will ([a]\cup[b]) be a single equivalence class?On (A={1,2,3,4,5}), (aRb) holds when (a) and (b) are both greater than (2) or both not greater than (2). Which partition is formed by this relation?On the set of all subsets of (S={1,2,3}), (A R B) holds when (A) and (B) have the same number of elements. Which is the equivalence class of ({1,2})?