Mathematics
Transitive relation
Practice questions
On A={1,2,3,4}, let R={(1,2),(2,3),(1,3),(3,4),(1,4),(2,4)}. What is the nature of R?On (A={1,2,3,4}), (R={(1,2),(2,4),(4,3),(1,4),(2,3)}). Which ordered pair must be added to make it transitive?On integers, (aRb) is defined when (a-b) is divisible by (7). Why is this relation transitive?On real numbers, (aRb) is defined when (a<b+2). This relation is not transitive. Choose the correct counterexample.On (A={1,2,3,4,5}), (R={(a,b):b-a=1}). What is the nature of this relation?On (A={1,2,3,4,6,12}), (aRb) is defined when (a) divides (b). What is the nature of this relation?On (A={1,2,3,4}), (R={(1,2),(2,1),(1,1),(2,2),(3,4),(4,3)}). Why is this relation not transitive?On real numbers, (aRb) is defined when (a^3\le b^3). Is this relation transitive?On (A={1,2,3,4,5,6}), (R={(a,b):a\equiv b \pmod{3}}). What is the nature of this relation?On (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,3)}). What is the correct reason for failure of transitivity?A relation (R) on a set is transitive. If ((a,b) \in R), ((b,c) \in R), and ((c,d) \in R), which ordered pair must definitely be in (R)?On (A={1,2,3,4,5}), (R={(a,b):a+b\text{ is even}}). Why is this relation transitive?On (A={1,2,3,4,5}), (R={(a,b):a+b\text{ is odd}}). What is the nature of this relation?On real numbers, (aRb) is defined when (|a|\ge |b|). Is this relation transitive?On (A={1,2,3,4}), (R={(1,2),(2,3),(3,4),(1,3),(2,4)}). Which pair is necessary to add to make it transitive?On a set of lines, (lRm) is defined when (l) and (m) are parallel in the same plane. For distinct lines, what is the nature of this relation?On the set of students of a school, (aRb) is defined when (a) and (b) have the same date of birth. What is the nature of this relation?On (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(2,3),(3,2)}). Which added pair would fix one failure of transitivity?On real numbers, (aRb) is defined when (a=b) or (a<b). Which standard relation is this, and what is its nature?On (A={1,2,3,4,5}), (R={(a,b):a<b\text{ and }a,b\text{ are both even}}). What is the nature of this relation?