Mathematics
Transitive relation
Practice questions
On the set (A={1,2,3}), the relation (R={(1,1),(1,2),(2,2),(2,3),(1,3),(3,3)}) is given. Is (R) transitive?On (A={1,2,3}), (R={(1,2),(2,3),(1,1),(2,2),(3,3)}). Why is (R) not transitive?Consider the relation (R={(a,b):a) divides (b}) on the set of natural numbers. What type of relation is it?On the set of integers, the relation (R={(a,b):a-b\text{ is even}}) is given. Is (R) transitive?On real numbers, the relation (R={(a,b):a<b}) is given. Choose the correct statement about this relation.On real numbers, the relation (R={(a,b):a\le b}) is given. Is it transitive?On (A={1,2,3,4}), (R={(1,2),(2,4),(1,4),(3,3)}). Which pair is most necessary in checking transitivity?On (A={a,b,c}), (R={(a,b),(b,c),(a,c),(b,b)}). What is the correct conclusion?On (A={1,2,3}), the empty relation (R=\varnothing) is given. Is (R) transitive?On (A={1,2,3}), the universal relation (R=A\times A) is given. Is this relation transitive?On (A={1,2,3,4}), (R={(1,2),(2,3),(3,4),(1,3),(2,4)}). Which pair must be added to make (R) transitive?On integers, (R={(a,b):a-b) is divisible by (3)(}). Is (R) transitive?On (A={1,2,3}), (R={(1,2),(2,1)}). Is (R) transitive?If a relation (R) contains ((2,5)) and ((5,7)), which pair must be present for (R) to be transitive?On (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4)}). Is this relation transitive?On real numbers, (R={(a,b):a=b}). Choose the correct option.On real numbers, (R={(a,b):a\ne b}). Is (R) transitive?On (A={1,2,3}), (R={(1,2),(2,3),(1,3),(3,1)}). Is (R) transitive?If (R) and (S) are transitive relations on a set, what can be said about (R \cap S)?Is the union (R \cup S) of two transitive relations (R) and (S) always transitive?