Mathematics
Transitive relation
Practice questions
On real numbers, (aRb) if (a<b<a+2). Is the relation transitive?On real numbers, (aRb) if (a-b) is rational. What type of relation is (R)?On real numbers, (aRb) if (a-b) is irrational. What type of relation is (R)?On (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1)}). Is (R) transitive?If (R) is an equivalence relation on a set, what can be said about its transitive property?If (R={(a,b):a,b\in\mathbb{N}\text{ and }a\mid b}), what is the correct reason for (R) being transitive?If (R={(a,b):a,b\in\mathbb{R}\text{ and }a^3=b^3}), what type of relation is (R)?If (R={(1,2),(2,3),(3,3),(1,3),(3,2),(2,2)}), is (R) transitive or not?If (R={(1,2),(2,3),(3,2),(2,2)}), why is (R) not transitive?What is the most common difficult mistake while checking a transitive relation?On (A={1,2,3,4}), (R={(1,2),(2,1),(1,1),(2,2),(2,4),(1,4)}). Is (R) transitive?If (R={(1,3),(3,2),(2,4),(1,2),(3,4)}), (R) is not transitive because which pair is missing?On integers, (aRb) if (a-b) is divisible by (6). What type of relation is (R)?On real numbers, (aRb) if (a^2\le b^2). Is this relation transitive?On real numbers, (aRb) if (a^2<b^2). Which statement is correct for (R)?If (R={(a,b):a,b\in\mathbb{R}\text{ and }a=b^2}), is (R) transitive?On a family of sets, (A,R,B) if (A\supseteq B). What type of relation is this?On sets, (A,R,B) if (A\subset B), where (A) is a proper subset. What type of relation is (R)?If (R={(1,4),(4,2),(2,2),(1,2),(4,4)}), what is the correct statement about (R)?If (R={(1,4),(4,2),(2,1),(1,2),(4,1)}), (R) is not transitive because which pair is missing?