Mathematics
Transitive relation
Practice questions
On (A={1,2,3,4,6,12}), (aRb) if the greatest common divisor of (a) and (b) is (a). This relation corresponds to which idea?On (A={1,2,3,4}), (R={(1,2),(2,3),(3,4),(1,3),(2,4)}). Which pair is necessarily needed to make (R) transitive?On real numbers, (aRb) if (a\le b+2). Is this relation transitive?On (A={1,2,3,4}), (R={(a,b):a\ge b}). Choose the correct statement for (R).On the set of students of a school, (aRb) if (a) and (b) study in the same class. Choose the correct option about transitivity of (R).On (A={1,2,3,4,5}), (R={(a,b):a+b\text{ is odd}}). Choose the correct conclusion about (R).On (A={1,2,3,4,5,6}), (aRb) if (a) and (b) have the same remainder when divided by (2). What is (R)?On (A={1,2,3,4}), (R={(1,2),(2,1),(1,1),(2,2),(3,4)}). Choose the correct statement about (R).On (A={1,2,3,4}), (R={(1,2),(2,3),(3,1),(1,3)}). Which pair is definitely required to satisfy transitivity?On real numbers, (aRb) if (a-b) is an integer. Choose the correct option about (R).On (A={1,2,4,8,16}), (aRb) if (b/a) is an integer. What is the correct conclusion for (R)?On integers, (aRb) if (a+b) is divisible by (4). Is this relation transitive?On (A={1,2,3,4,5}), (R={(a,b):a<b\text{ and }a+b\text{ is odd}}). Which statement about (R) is correct?On a set (A), (R) is transitive and (R\subseteq S). Is it certain that (S) is transitive?On (A={1,2,3}), (R={(1,1),(1,2),(2,2),(2,3),(1,3),(3,3)}). What is (R)?On (A={1,2,3,4}), (R={(1,2),(2,4),(1,4),(4,2)}). Which pair is necessarily required for transitivity?On real numbers, (aRb) if (a=b) or (a<b). Choose the correct option for (R).On integers, (aRb) if (a-b) is even and (a\le b). Choose the correct statement about (R).On (A={1,2,3,4}), (R={(1,3),(3,3),(3,4),(1,4),(4,4)}). Choose the correct conclusion about (R).On real numbers, (aRb) if (a^3\le b^3). Which option about transitivity of (R) is correct?