Mathematics
Equivalence relation
Practice questions
On the set (A={1,2,3,4}), relation (R) is defined by (aRb) when (a) and (b) are both even or both odd. What type of relation is (R)?On (A={1,2,3,4,5,6}), (aRb) when (a \equiv b \pmod{3}). Which is the equivalence class of (4)?On (A={a,b,c}), (R={(a,a),(b,b),(c,c),(a,b),(b,a)}) is given. What type of relation is it?On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)}). Why is it not an equivalence relation?Which option is correct for calling a relation (R) an equivalence relation?On integers, (aRb) when (a-b) is divisible by (4). What type of relation is this?On (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(1,2),(2,1)}). Why is it not an equivalence relation?If (R) is an equivalence relation and ((x,y)\in R), which pair must belong to (R)?If (R) is an equivalence relation and ((p,q)\in R), ((q,r)\in R), which pair will definitely belong to (R)?On (A={1,2,3,4,5}), (aRb) when (a) and (b) give the same remainder on division by (5). What is the equivalence class of (5)?On (A={1,2,3,4}), (aRb) when (a+b) is even. Choose the correct statement.What is correct about classes formed by an equivalence relation?If (R) is an equivalence relation and (a) is an element of a set, which elements come in ([a])?On real numbers, (aRb) when (|a|=|b|). Which statement about (R) is correct?On (A={1,2,3,4,5,6,7,8}), (aRb) when (a) and (b) leave the same remainder on division by (4). How many equivalence classes are formed?On (A={1,2,3,4}), the universal relation (R=A\times A) is given. What type of relation is it?On the non-empty set (A={1,2}), the empty relation (R={}) is given. Is (R) an equivalence relation?If (R={(a,a):a\in A}), how can (R) be identified?On (A={1,2,3,4,5}), relation (R) forms two classes ({1,5}), ({2,3,4}). Which pair must belong to (R)?On (A={1,2,3,4,5}), relation (R) forms the classes ({1,5}), ({2,3,4}). Which pair will not belong to (R)?