Mathematics
Transitive relation
Practice questions
On (A={1,2,3,4}), (R={(1,2),(2,3),(3,4)}). What is the first clear reason that (R) is not transitive?The relation (R={(a,b):a) and (b) have the same age(}) is defined on a set of people. Is it transitive?On a set of students, (R={(a,b):a) is a friend of (b)(}). Is this relation generally transitive?On A={1,2,3}, let R={(1,2),(2,2),(2,3),(1,3)}. Is R transitive?If (R) is transitive and ((4,6)\in R), ((6,9)\in R), which conclusion is certain?On (A={1,2,3}), (R={(1,1),(1,2),(2,1),(2,2),(3,3)}). Which statement about (R) is correct?On (A={1,2,3,4}), relation (R={(a,b):a\le b}). From ((2,3)) and ((3,4)), which pair follows by transitivity?A relation (R) on a set (A) is transitive. If ((x,y)\in R) and ((y,z)\in R), which statement is correct?On (A={1,2,3,4}), (R={(1,2),(2,3),(1,3),(3,4),(1,4),(2,4)}). What is the correct conclusion about (R)?On integers, (R={(a,b):a \equiv b \pmod{5}}). Why is this relation transitive?On (A={1,2,3}), (R={(1,1),(1,2),(2,2),(3,3),(2,3)}). What must be done to make (R) transitive?Which statement gives the correct definition of a transitive relation (R)?On (A={1,2,3,4}), (R={(1,2),(2,2),(2,4),(1,4),(4,4)}). Is (R) transitive?The relation (R={(a,b):a) is the father of (b)(}) is defined on a set of people. Is it generally transitive?On real numbers, (R={(a,b):a>b}) is given. Is it transitive?On (A={1,2,3}), (R={(1,2),(2,3),(3,1),(1,3)}). Choose a correct reason why (R) is not transitive.If (R={(1,2),(2,3),(1,3),(3,3)}), which pair can be added without creating a new transitivity requirement?On (A={1,2,3}), (R={(1,1),(1,2),(2,3),(1,3),(2,2)}). Which statement is correct?The relation (R={(a,b):a) is greater than or equal to (b)(}) is defined on real numbers. Is it transitive?On (A={1,2,3,4}), (R={(1,3),(3,4),(1,4),(2,2)}). Is (R) transitive?