Mathematics
Transitive relation
Practice questions
On (A={1,2,3,4,5}), (R={(a,b):|a-b|\le 1}). Choose the correct statement about (R).On a set (A), the identity relation (I={(a,a):a\in A}) is given. Choose the correct option about (I).On (A={1,2,3,4}), (R={(1,2),(2,2),(2,3),(1,3),(3,2)}). Why is (R) not transitive?On natural numbers, (aRb) if (b=2a). What is the correct conclusion about (R)?On (A={1,2,3,4,5,6}), (aRb) if (a) and (b) leave the same remainder on division by (3). Choose the correct option for (R).On (A={1,2,3,4}), (R={(1,1),(1,2),(2,3),(1,3),(3,4),(1,4),(2,4)}). Choose the correct statement.On real numbers, (aRb) if (a<b+1). What is the correct conclusion for (R)?On a set (A), (R) is a transitive relation. Which statement about (R^{-1}) is always true?On (A={1,2,3,4,5}), (aRb) if (a\le b) and (b-a\le2). Choose the correct statement about (R).On integers, (aRb) if (a=b) or (a-b) is divisible by (5). Choose the correct option about transitivity of (R).On the set (A={1,2,3}), the relation (R={(1,1),(1,2),(1,3),(2,2),(2,3),(3,3)}) is given. What type of relation is it?On the set (A={1,2,3}), the relation (R={(1,2),(2,3),(1,1)}) is given. Which ordered pair must be added at minimum to make it transitive?On the set of integers, (aRb) is defined when (a-b) is divisible by (3). What is the nature of this relation?On real numbers, (aRb) is defined when (a<b). Why is this relation transitive?On real numbers, (aRb) is defined when (a\le b). Choose the correct statement.On non-zero integers, (aRb) is defined when (a) divides (b). What is the nature of this relation?On (A={1,2,3,4}), (R={(1,2),(2,4),(1,4),(3,4)}). What is the correct conclusion about this relation?On (A={1,2,3}), (R={(1,2),(2,1)}). Why is this relation not transitive?What is the nature of the empty relation (\varnothing) on any non-empty set (A)?Why is the universal relation (A\times A) transitive on any set (A)?