Mathematics
Equivalence relation
Practice questions
If (R) is an equivalence relation on (A), with what will every element (a\in A) be related?If both (aRb) and (bRa) are true, which property does this indicate?If (aRb), (bRc), and therefore (aRc) are true, which property is shown?On (A={2,4,6,8}), (aRb) when (a) and (b) are both divisible by (2). What type of relation is (R)?On (A={1,3,5,7}), (aRb) when (a+b) is even. What type of relation is (R)?On (A={1,2,3}), (aRb) when (a=b) or both are from (1) and (2). What type of relation is (R)?If (R) is an equivalence relation, which type of missing part should not occur in (R)?On (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,4),(4,1)}). What is the equivalence class of (1)?What is the safest stepwise method to check an equivalence relation in a school exam?On the set of triangles, a relation is defined such that two triangles are related when they have the same area. What type of relation is this?On the set (A={1,2,3}), the relation (R={(1,1),(2,2),(3,3),(1,2),(2,1)}) is given. Which pair must be added to make it an equivalence relation?On integers, (aRb) is defined when (a-b) is divisible by (4). What is the equivalence class of (7)?On (A={1,2,3,4}), (aRb) holds when (a) and (b) are both even or both odd. What are the equivalence classes?Which property of an equivalence relation requires that if ((a,b)\in R) and ((b,c)\in R), then ((a,c)\in R)?On real numbers, (aRb) holds when (a-b=0). What type of relation is it?On (A={1,2,3,4,5,6}), (aRb) holds when (a\equiv b \pmod{3}). How many equivalence classes are formed?When is a relation (R) on a set (A) called an equivalence relation?For (A={1,2,3}), which statement is correct about the universal relation (R=A\times A)?Why is the empty relation (\varnothing) on (A={1,2,3}) not an equivalence relation?On integers, (aRb) holds when (a+b) is even. What type of relation is this?