Mathematics
Transitive relation
Practice questions
On real numbers, (aRb) is defined when (a^2\le b^2). Which statement is correct?On (A={1,2,3,4,5}), (R={(a,b):a+b=6}). Which counterexample correctly tests transitivity?On (A={1,2,3,4,5,6}), (R={(a,b):a\le b\text{ and }a,b\text{ are in the same remainder class when divided by }3}). What is the nature of this relation?On (A={1,2,3,4}), (R={(1,2),(2,3),(3,1),(1,3),(2,1)}). Which is a failure of transitivity?On real numbers, (aRb) is defined when (a\le b+1). This relation is not transitive. Choose the correct example.On (A={1,2,3,4,5}), (R={(a,b):a) and (b) are both less than (5)(}). Is this relation transitive?On real numbers, (aRb) is defined when (a^2+b^2=0). What is the nature of this relation?On (A={1,2,3,4,5,6}), (R={(a,b):a\mid b\text{ and }b\mid a}). What is the nature of this relation?On (A={1,2,3,4,5}), (R={(a,b):a\ne b}). Is this relation transitive?On a set, (R) and (S) are both transitive relations. Which statement is always true?On (A={1,2,3,4,5}), the relation (R={(1,2),(2,5),(1,5),(3,4)}) is given. Is this relation transitive?On (A={1,2,3,4,5}), (R={(1,3),(3,5),(2,4),(1,5)}). Which conclusion is correct?On (A={1,2,3,4,5}), (R={(1,2),(2,4),(4,5),(1,4),(2,5)}). Which pair must be added to make it transitive?On integers, (aRb) is defined when (a-b) is divisible by (9). What is the nature of this relation?On real numbers, (aRb) is defined when (a+2\le b+2). Which standard relation is this equivalent to, and what is its nature?On natural numbers, (aRb) is defined when (b=3a). Is this relation transitive?On (A={1,2,3,6,9,18}), (aRb) is defined when (a) divides (b). Which statement is correct?On (A={1,2,3,4}), (R={(1,2),(2,1),(1,1),(3,4),(4,3),(3,3),(4,4)}). Why is this relation not transitive?On (A={1,2,3,4,5}), (R={(a,b):a\le b\text{ and }b-a\text{ is divisible by }2}). What is the nature of this relation?On real numbers, (aRb) is defined when (a^4\le b^4). Is this relation transitive?