Mathematics
Transitive relation
Practice questions
On (A={1,2,3,4}), (R={(1,2),(2,4),(1,4),(4,4)}). Choose the correct option for (R).If (R={(1,2),(2,4),(1,4),(4,1)}), is (R) transitive?What is the nature of the universal relation (A\times A) on any non-empty set (A)?On (A={1,2,3}), (R={(1,1),(1,2),(2,2),(2,3)}). Which pair must be added to make it transitive?If (R={(a,b):a,b \in \mathbb{Z}\text{ and }a-b\text{ is even}}), what type of relation is (R)?If (R={(a,b):a,b \in \mathbb{Z}\text{ and }a-b\text{ is odd}}), is (R) transitive?On (\mathbb{R}), the relation (aRb) if (a=b) is transitive or not?If (R={(1,1),(1,2),(2,2),(2,1)}), choose the correct statement about (R).Which of the following relations is generally transitive?If a relation is symmetric, must it always be transitive?If (R) is transitive and ((x,y) \in R), ((y,z) \in R), what is the correct conclusion?On A = {1, 2, 3}, let R = {(1,2), (2,2), (2,3), (1,3)}. Is R transitive?If (R={(1,2),(2,2),(2,3)}), why is (R) not transitive?What type is the relation (R={(a,b):a,b \in \mathbb{N}\text{ and }a\text{ is a multiple of }b})?A relation (R) on a set (A) is transitive. If ((2,5)), ((5,7)), and ((7,9)) are all in (R), which pair must definitely be in (R)?Which of the following relations is not transitive?If (R) is transitive, which statement is correct?On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2)}). Is (R) transitive?If (R={(1,2),(2,3),(3,1)}), which pair is first clearly required to make it transitive?On integers, (aRb) if (a \equiv b \pmod{3}). What type of relation is (R)?