Mathematics
Equivalence relation
Practice questions
If two equivalence classes have even one common element, what is correct about them?On real numbers, (aRb) when (a^2=b^2). Why is this an equivalence relation?On (A={-2,-1,1,2}), (aRb) when (|a|=|b|). What is the equivalence class of (-2)?Which relation is generally an equivalence relation?Which relation does not form an equivalence relation?On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,3)}). Why is it not an equivalence relation?If a relation is reflexive and transitive but not symmetric, what will it be?If a relation is symmetric and transitive but not reflexive, what is the correct conclusion about equivalence relation?On (A={1,2,3,4,5,6}), (aRb) when (a) and (b) are both divisible by (2) or both not divisible by (2). Which is the class of (2)?On (A={1,2,3,4,5,6}), (aRb) when (a) and (b) leave the same remainder on division by (2). What is the equivalence class of (3)?What is correct about two elements inside the same class formed by an equivalence relation?If (a) and (b) are in different equivalence classes, what is correct about ((a,b))?On (A={1,2,3}), how many ordered pairs will be in (R=A\times A)?What is the correct meaning of the reflexive property in an equivalence relation?What is the correct meaning of the symmetric property in an equivalence relation?What is the correct meaning of the transitive property in an equivalence relation?On (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(1,3),(3,1)}). Why is it not an equivalence relation?On integers, (aRb) when (a\equiv b \pmod{2}). Which classes are formed?On (A={0,1,2,3,4,5}), (aRb) when (a \equiv b \pmod{3}). What is the equivalence class of (0)?The set (A={1,2,3,4}) is divided into parts ({1}), ({2,4}), ({3}). What type of relation is formed from this partition?