Mathematics
Equivalence relation
Practice questions
The set (A={1,2,3,4}) is divided into parts ({1,3}) and ({2,4}). What type of relation is being in the same part?How does an equivalence relation organize a set?If (R) is an equivalence relation, what generally forms the equivalence class of (a)?On integers, (aRb) when (a \equiv b \pmod{3}). What type of relation is this?On integers, (aRb) when (a+b) is even. Choose the correct conclusion.On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2)}). Why is it not an equivalence relation?Which property checks that for every (a\in A), ((a,a)\in R)?Which is the correct identification of the symmetric property?Which is the correct identification of the transitive property?On (A={1,2,3,4}), (R) contains pairs whose two numbers have the same remainder on division by (2). What is the equivalence class of (1)?On (A={0,1,2,3,4,5}), (aRb) when (a \equiv b \pmod{3}). Which is the equivalence class of (2)?Which relation is the best example of an equivalence relation?Which relation is generally not an equivalence relation?On natural numbers, (aRb) when (a=b). What type of relation is (R)?On real numbers, (aRb) when (|a|=|b|). What type of relation is this?On real numbers, (aRb) when (a^2=b^2). Choose the correct statement.On (A={1,2,3,4,5,6}), (aRb) when (a) and (b) leave the same remainder on division by (3). How many equivalence classes does (R) form?If (R) is an equivalence relation, which statement about two equivalence classes is correct?If a relation is an equivalence relation, must it be reflexive?If a relation is an equivalence relation, must it be symmetric?