Mathematics
Equivalence relation
Practice questions
In (A={1,2,3,4}), for the same parity relation, what is the equivalence class of (2)?If (aRb) means objects (a) and (b) have the same color, what type of relation can it be on a set of objects?On (A={1,2,3}), why is (R={(1,1),(2,2),(3,3),(1,2)}) not an equivalence relation?On (A={1,2,3}), why is (R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}) not an equivalence relation?Which relation is called the identity relation?Which relation is called the universal relation?If (R) is an equivalence relation, from which property do we get ((a,a)\in R)?If (R) is an equivalence relation and ((4,7)\in R), why must ((7,4)\in R)?If (R) is an equivalence relation and ((1,2)\in R), ((2,5)\in R), which pair must be present?On integers, (aRb) if (a\equiv b \pmod{2}). What is the equivalence class of (0)?On integers, (aRb) if (a\equiv b \pmod{2}). What is the equivalence class of (1)?In (A={1,2,3,4,5,6}), (aRb) if (a) and (b) have the same remainder when divided by (3). What is the class of (1)?In (A={1,2,3,4,5,6}), under the same remainder modulo (3) relation, what is the equivalence class of (2)?In (A={1,2,3,4,5,6}), under the same remainder modulo (3) relation, what is the equivalence class of (3)?On (A={1,2,3,4}), what type of relation is (R={(1,1),(2,2),(3,3),(4,4),(1,3),(3,1),(2,4),(4,2)})?If the equivalence classes of an equivalence relation are {(1,2)} and {(3)}, what is the original set?Which statement is true about two different equivalence classes formed by an equivalence relation?What are the equivalence classes of the identity relation on a set?What are the equivalence classes of the universal relation on a set?If (R) is an equivalence relation and ([a]\neq[b]), what is ([a]\cap[b])?