Mathematics
Transitive relation
Practice questions
If (R) is transitive and ((p,q)\in R), ((q,r)\in R), ((r,s)\in R), ((s,t)\in R), which pair must definitely be in (R)?If (R) and (S) are transitive and (R\subseteq S), which statement about (S\setminus R) is correct?If (R={(1,2),(2,3),(1,3)}) and (S={(1,3),(3,4),(1,4)}), what type is (R\cup S)?If (R) is transitive, what can be said about (R\circ R\subseteq R)?If for a relation (R), (R\circ R\subseteq R), what is the correct conclusion about (R)?If (R={(1,2),(2,3),(1,3),(3,5),(1,5),(2,5)}), what type of relation is (R)?If (R={(1,2),(2,5),(5,3),(1,5),(2,3)}), which pair is immediately required to make it transitive?On natural numbers, (aRb) if (a) and (b) have a common divisor, that is (\gcd(a,b)>1). Is this relation transitive?On natural numbers, (aRb) if (a) and (b) are coprime. Is (R) transitive?On real numbers, (aRb) if (a-b) is an integer. What type of relation is (R)?If (R={(a,b):a,b\in\mathbb{R}\text{ and }a-b>2}), is (R) transitive?If (R={(a,b):a,b\in\mathbb{R}\text{ and }0<a-b<2}), what type is (R)?If (R) is transitive and ((1,2),(2,3),(3,1)\in R), which of these pairs must necessarily be in (R)?If (R) is transitive and contains ((1,2),(2,3),(3,1)), toward what does the whole ({1,2,3}) part move?On (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,3),(3,1)}). Is (R) transitive?If (R={(1,1),(3,3),(1,3),(3,1),(2,4)}), which option is correct for (R)?If (R={(1,3),(3,1),(1,1),(2,4)}), why is (R) not transitive?If (R) is transitive and contains ((a,b)), ((b,c)), and ((c,a)), which statement is correct?On real numbers, (aRb) if (a\le 2b). Is this relation transitive?On real numbers, (aRb) if (a=kb), where (k) is a fixed positive real number. In which case will this relation always be transitive?