Mathematics
Equivalence relation
Practice questions
Which three properties must a relation have to be an equivalence relation?Why is the universal relation on (A={1,2,3}) always reflexive?Why is the empty relation on (A={1,2,3}) not an equivalence relation?If (R) is an equivalence relation and ((a,b)\in R), ((b,c)\in R), which conclusion is correct?On integers, (aRb) if (a-b) is even. What kind of relation is this?On integers, (aRb) if (a\equiv b \pmod{3}). How many equivalence classes are there?For a relation (aRb) if (a=b), what type of relation is it on any set?On (A={1,2,3}), (R=A\times A). What kind of relation is it?If ((a,a)\in R) for every (a\in A), which property is this?If ((a,b)\in R) always implies ((b,a)\in R), which property is this?If ((a,b)\in R) and ((b,c)\in R) always imply ((a,c)\in R), which property is this?On (A={1,2,3}), why is (R={(1,1),(2,2),(3,3),(1,2),(2,1)}) not an equivalence relation?On (A={1,2,3}), why is (R={(1,1),(2,2),(1,2),(2,1)}) not an equivalence relation?On natural numbers, (aRb) if (a) and (b) are both even or both odd. What is this relation?On integers, (aRb) if (a-b) is divisible by (5). This relation is connected with which idea?If (aRb) means students (a) and (b) study in the same class, what type of relation is it on a set of students?If (aRb) means (a) and (b) have birthdays on the same date, what type of relation is it?An equivalence relation divides a set into what?If (R) is an equivalence relation, what is the equivalence class of an element (a)?In (A={1,2,3,4}), for the same parity relation, what is the equivalence class of (1)?