Mathematics
Transitive relation
Practice questions
If (R) is transitive, what about (R\cup\Delta), where (\Delta={(a,a):a\in A})?If (R) is not transitive, will (R\cup\Delta) always become transitive?If (R={(1,2),(2,3),(3,4),(1,3),(2,4),(1,4),(4,4)}), what type of relation is (R)?If (R={(1,2),(2,3),(3,4),(1,3),(2,4)}), which missing pair breaks transitivity?On real numbers, (aRb) if (a-b\in\mathbb{Q}). What type will (R^{-1}) be?If (R) is transitive and (S) is the identity relation, what is correct about (R\cap S)?If (R={(1,1),(1,2),(2,2)}) and (S={(2,2),(2,3),(3,3)}), what type is (R\cup S)?If (R={(1,1),(1,2),(2,2)}) and (S={(2,2),(2,3),(3,3)}), what type is (R\cap S)?If (R={(a,b):a,b\in\mathbb{R}\text{ and }a^2+b^2=0}), what type is (R)?On real numbers, (aRb) if (ab>0). Is this relation transitive?On real numbers, (aRb) if (ab<0). What type is (R)?If (R={(1,2),(2,4),(4,8),(1,4),(2,8),(1,8)}), what is the correct conclusion for (R)?If (R={(1,2),(2,4),(4,8),(1,4),(2,8)}), which pair should be added to fill the main transitivity gap?If (R) is transitive and contains ((x,y)) and ((y,y)), which conclusion is correct?If (R) is transitive and contains ((x,x)) and ((x,y)), which conclusion is correct?If (R={(1,1),(1,2),(2,2),(3,1),(3,2)}), is (R) transitive?If (R={(1,1),(1,2),(2,2),(3,1)}), which pair must be added to make it transitive?If (R) is missing a pair ((a,b)), does that alone prove (R) is not transitive?If (R={(2,3),(3,5),(5,2)}) is to be made transitive, which pairs arise in the first layer?At hard level, what is the best written method to check a transitive relation?