Mathematics
Transitive relation
Practice questions
On natural numbers, (aRb) is defined when (b=2a). Is this relation transitive?On (A={1,2,4,8}), (aRb) is defined when (b) is a multiple of (a). What is the nature of this relation?On (A={1,2,3}), (R={(1,2),(2,1),(1,1),(2,2),(2,3)}). What is the correct reason for failure of transitivity?A relation (R) on a set is transitive. If ((p,q) \in R), ((q,r) \in R), and ((r,s) \in R), which pair must definitely be in (R)?On (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,3),(1,3),(3,4),(1,4),(2,4)}). What is the nature of this relation?On real numbers, (aRb) is defined when (|a|\le |b|). Is this relation transitive?On real numbers, (aRb) is defined when (a<b+1). Is this relation transitive?On (A={1,2,3,4}), (R={(a,b):a\le b\text{ and }b-a\le 1}). What is the nature of this relation?On (A={2,3,4,6,12}), (aRb) is defined when (a) divides (b). Which statement correctly proves transitivity?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 transitive?On integers, (aRb) is defined when (a \equiv b \pmod{5}). Is this relation transitive?On (A={1,2,3,4,5,6}), (R={(a,b):a\equiv b \pmod{2}}). What is the nature of this relation?On (A={1,2,3,4}), (R={(1,2),(2,4),(1,4),(2,2),(4,4),(1,1)}). Which check correctly supports transitivity?On the set of students in a class, (aRb) is defined when student (a) has the same age as student (b). What is the nature of this relation?On a set of lines, (lRm) is defined when line (l) is parallel to line (m). For distinct lines in the same plane, why is this relation considered transitive?On (A={1,2,3,4,5}), (R={(a,b):a<b\text{ and }a,b\text{ are both odd}}). What is the nature of this relation?On (A={1,2,3,4}), (R={(a,b):a+b\text{ is odd}}). This relation is not transitive. Which is the correct counterexample?On (A={1,2,3,4}), (R={(1,2),(2,3),(3,4),(1,3),(2,4),(1,4)}). Why is this relation transitive?On (A={1,2,3,4,5}), (R={(a,b):a) is less than (b) and (b-a) is even(}). What is the nature of this relation?On (A={1,2,3,4}), (R={(1,1),(1,2),(2,2),(3,3),(4,4),(2,1)}). Is this relation transitive?