Mathematics
Transitive relation
Practice questions
If a relation contains ((1,2)), ((2,3)), and ((3,4)), which pair will also be necessary for full transitivity?On (A={1,2,3}), (R={(1,2),(2,2),(2,3),(1,3)}). Is it transitive?If (R) is transitive and ((5,6)\in R), ((6,8)\in R), which conclusion is correct?What is the correct decision about (R={(1,1),(1,2),(2,2)}) based on transitivity?Which statement about a transitive relation is false?On (A={1,2,3,4}), (R={(1,2),(2,4),(1,4),(3,3)}). Is (R) transitive?On (A={1,2,3}), (R={(1,2),(2,1),(1,1)}). Why is (R) not transitive?In a relation (R), ((a,b)\in R), ((b,c)\in R), and ((a,c)\notin R). What does this mean?On integers, (aRb) means (a\equiv b \pmod{2}). Is it transitive?On integers, (aRb) means (a-b) is even. What type of relation is it?On real numbers, (aRb) means (a\ge b). Is this relation transitive?On real numbers, (aRb) means (a\ne b). Is this relation transitive?On a set of students, (aRb) means (a) and (b) have the same age. What type of relation is it?On a set of persons, (aRb) means (a) is brother of (b). Is it generally transitive?For lines in a plane, (lRm) means (l\parallel m). Is it transitive?For lines in a plane, (lRm) means (l\perp m). Is it transitive?If (R) is transitive and ((p,q)\in R), ((q,r)\in R), ((r,s)\in R), which listed pair must definitely be in (R)?On (A={1,2,3}), (R={(1,2),(2,3),(1,3),(2,2)}). Which extra pair is not required while checking transitivity?In which situation can a relation be proved non-transitive?If a relation has only one pair ((2,3)), why is it transitive?