Mathematics
Transitive relation
Practice questions
On real numbers, (aRb) if (a^2=b^2). What type of relation is (R)?On real numbers, (aRb) if (a=b+1). Is this relation transitive?On real numbers, (aRb) if (a-b\ge 0). What type of relation is it?On a family of sets, (A,R,B) if (A\subseteq B). What type of relation is (R)?On sets, (A,R,B) if (A\cap B=\varnothing). Is this relation transitive?If (R={(a,b):a,b\in\mathbb{R}\text{ and }|a|=|b|}), choose the correct option for (R).If (R={(a,b):a,b\in\mathbb{R}\text{ and }|a-b|<1}), is (R) transitive?If (R={(a,b):a,b\in\mathbb{R}\text{ and }a\le b+2}), is (R) transitive?On (A={1,2,3,4,5}), (aRb) if (a\le b). What type of relation is this?If a relation (R) contains ((1,2),(2,3),(3,4)) and (R) is transitive, which group must definitely be in (R)?If (R) is transitive and (R\subseteq S), is (S) always transitive?If (S) is transitive and (R\subseteq S), is (R) always transitive?If (R={(1,2),(2,3),(1,3),(3,2)}), what is the correct reason that (R) is not transitive?If (R={(1,2),(2,3),(1,3),(3,2),(2,2),(3,3)}), what type is (R)?What is the safest method to prove transitivity in hard relation questions?If (R) is transitive and ((a,b)\in R), ((b,a)\in R), which conclusion is definite?If a relation (R) contains ((1,2),(2,1)) but not ((1,1)), what can be said about (R)?If (R=\varnothing) on a non-empty set (A), which statement about (R) is correct?If a relation contains only ((1,2)) and ((3,4)), is it transitive or not?If (R={(1,2),(2,3),(3,4),(1,3),(2,4)}), which pair must be added to make it transitive?