Mathematics
Transitive relation
Practice questions
Which is the correct definition of a transitive relation?On (A={1,2,3}), (R={(1,2),(2,3),(1,3)}) is given. Is (R) transitive?On (A={1,2,3}), (R={(1,2),(2,3)}). Why is (R) not transitive?On natural numbers, relation (R) is defined by (aRb) if (a\le b). What is (R)?On real numbers, (R={(a,b):a<b}). Is (R) transitive?On (A={1,2,3}), (R={(1,1),(2,2),(3,3)}) is given. Choose the correct statement about (R).Is the empty relation (\varnothing) on a set (A) transitive or not?Why is the universal relation (A\times A) on a set (A) transitive?On (A={1,2,3,4}), (R={(1,2),(2,4),(1,4)}). Is (R) transitive or not?On (A={1,2,3,4}), which pair must be added to make (R={(1,2),(2,4)}) transitive?On integers, relation (R) is defined by (aRb) if (a=b). What type of relation is it?On (A={1,2,3}), (R={(1,2),(2,1)}). Why is (R) not transitive?On (A={1,2,3}), (R={(1,2)}). Choose the correct statement about (R).On natural numbers, (R={(a,b):a\mid b}). What is correct about (R)?On integers, (R) is defined by (aRb) if (a \equiv b \pmod{3}). What is (R)?On (A={1,2,3,4}), (R={(1,2),(2,3),(1,3),(3,4),(1,4),(2,4)}). Choose the correct statement about (R).On (A={1,2,3,4}), for (R={(1,2),(2,3),(3,4)}), which pair is clearly required first to make it transitive?If ((2,5) \in R) and ((5,7) \in R), and (R) is transitive, which pair must be in (R)?If (R) is transitive and ((3,3) \in R), which conclusion must follow?On (A={1,2,3}), (R={(1,1),(1,2),(2,2)}). Is (R) transitive or not?