Mathematics
Transitive relation
Practice questions
On a family of sets, define (A R B) if (A \subseteq B). Is this relation transitive?On a family of sets, define (A R B) if (A \cap B=\varnothing). Is this relation transitive?On the set of lines, (lRm) if line (l) is parallel to line (m). In a plane, what is this relation?On a set of people, (aRb) if (a) is brother of (b). In general, is this relation transitive?On (A={1,2,3}), (R={(1,1),(1,2),(2,3),(1,3),(3,3)}). Which check is most important for transitivity?On (A={1,2,3}), (R={(1,1),(1,2),(2,1),(2,2),(2,3),(1,3)}). Which pair is additionally needed to make (R) transitive?On (A={1,2,3}), (R={(1,2),(2,1),(2,3),(1,1),(1,3)}). Which pair must be added to make (R) transitive?On (A={1,2,3,4}), (R={(1,2),(2,3),(3,1),(1,3),(2,1),(3,2)}). Which missing pairs are most clearly needed to make (R) transitive?If (R) and (S) are both transitive relations, which statement about (R \cap S) is correct?If (R) and (S) are transitive, what is generally true about (R \cup S)?On (A={1,2,3}), (R={(1,2)}). Is (R) transitive?On (A={1,2}), (R={(1,2),(2,2)}). Is (R) transitive?On (A={1,2,3}), (R={(1,1),(1,2),(2,1)}). Why is it not transitive?On (A={1,2,3,4}), (R={(1,2),(2,3),(1,3),(3,4),(1,4),(2,4)}). Which transitivity chain is correct?On integers, (aRb) if (a \equiv b \pmod{3}). Is (R) transitive?On integers, (aRb) if (a+b) is even. Is (R) transitive?On integers, (aRb) if (a+b) is odd. Is (R) transitive?On (A={1,2,3,4}), (R={(1,3),(3,3),(3,4),(1,4)}). Is (R) transitive?Which option gives a relation that is definitely transitive?For (R={(1,2),(2,3),(1,3),(3,1)}), which pair is definitely needed to make it transitive?