Mathematics
Transitive relation
Practice questions
On (A={1,2,3,4}), (R={(1,2),(2,3),(1,3),(3,4),(2,4),(1,4)}). Choose the correct statement about (R).If (R={(1,2),(2,3),(1,3),(3,1)}), why is (R) not transitive?On integers, (aRb) if (a-b) is divisible by (4). What type of relation is it?If (R={(a,b):a,b\in\mathbb{Z}\text{ and }a+b\text{ is even}}), which option is correct for (R)?If (R={(a,b):a,b\in\mathbb{Z}\text{ and }a+b\text{ is odd}}), what type of relation is (R)?On (A={1,2,3}), (R={(1,1),(1,2),(2,2),(2,1),(2,3),(1,3)}). Is (R) transitive?In a relation like the previous one, what is the correct conclusion when every required pair is actually present?Which relation on A={1,2,3} is transitive but not reflexive?If (R={(1,2),(2,3),(3,1)}), which group must start getting added to form the full transitive closure?On integers, (aRb) if (a \equiv b \pmod{5}). Which statement is correct about (R)?On (A={1,2,3,4}), (R={(1,2),(2,4),(4,3),(1,4),(2,3)}). (R) is not transitive because which pair is missing?If (R) is transitive and ((2,5)\in R), ((5,8)\in R), ((8,11)\in R), which pair must definitely be in (R)?If (R) and (S) are both transitive relations on a set (A), what is correct about (R\cap S)?Is the union (R\cup S) of two transitive relations always transitive?If (R={(1,2)}) and (S={(2,3)}), both are transitive individually. What about (R\cup S)?If (R) is transitive, which statement is correct about (R^{-1})?If (R={(1,1),(1,2),(2,2),(2,3),(1,3),(3,3)}), what type will (R^{-1}) be?On (A={1,2,3,4}), (R={(1,2),(2,2),(2,4),(1,4),(4,4),(3,3)}). Choose the correct statement.If (R={(1,2),(2,4),(1,4),(4,2)}), (R) is not transitive because which pair is required?On natural numbers, (aRb) if (a) is a factor of (b). What type of relation is it?