Mathematics
Equivalence relation
Practice questions
If a relation is an equivalence relation, must it be transitive?On (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,4),(4,1)}). What is the correct statement about (R)?On (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(2,3),(3,2)}). Why is it not an equivalence relation?On (A={1,2,3}), the empty relation (R={}) is given. Is it an equivalence relation?If (A={}) and (R={}), which statement about (R) is correct?On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1),(1,3),(3,1),(2,3),(3,2)}). What relation is this?If a relation divides a set into the classes ({a,b}) and ({c}), which pairs must be present?If (R) is an equivalence relation and (aRb), what is correct about the equivalence classes of (a) and (b)?On integers, (aRb) when (a-b) is divisible by (5). Which statement about (R) is correct?On (A={1,2,3,4}), (aRb) when (a+b) is odd. Why is it not an equivalence relation?On (A={1,2,3}), (aRb) when (a\le b). Why is it not an equivalence relation?On (A={1,2,3}), (aRb) when (a<b). Why is it not an equivalence relation?On real numbers, (aRb) when (a-b=0). What type of relation is (R)?If (R) is an equivalence relation, what does ([a]) usually mean?On (A={1,2,3,4}), (R) forms two classes ({1,2}) and ({3,4}). Which pair will not belong to (R)?If (R) is reflexive, symmetric, and transitive, what is (R) called?On (A={1,2,3,4,5}), (aRb) when (a) and (b) give the same remainder on division by (2). What is the equivalence class of (4)?Which method is the most correct for checking an equivalence relation?On the set (A={1,2,3,4,5,6}), relation (R) is defined by (aRb) when (a) and (b) give the same remainder on division by (3). Which is the equivalence class of (1)?On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(2,3),(3,2)}) is given. What type of relation is this?