Mathematics
Symmetric relation
Practice questions
Which relation has symmetry but does not necessarily contain ((a,a)) for every element?If relation (R) is symmetric and transitive, and ((1,2)\in R), ((2,1)\in R), which pair can be obtained by transitivity?If (R) is symmetric and contains ((a,b)) where (a\ne b), which minimum pair must also be present to maintain symmetry?Which option gives a rule that will not form a symmetric relation?If (R) is symmetric, which of the following statements is not always true?For (R={(1,2),(2,1),(1,3),(3,1)}) on (A={1,2,3}), which statement is correct?If (R={(1,1),(2,2),(3,3),(1,2),(2,1)}), what type is (R) on (A={1,2,3})?Which option correctly shows a symmetric relation in matrix form?If (R) is symmetric and ((3,3)\in R), which extra pair is required because of ((3,3))?On (A={1,2,3,4}), what type is (R={(a,b):a\ne b})?On (A={1,2,3,4}), what type is (R={(a,b):a+b\le 5})?On (A={1,2,3,4}), in the relation (R={(a,b):a+b\text{ is odd}}), which pair must occur with ((1,2))?If a relation contains ((1,4),(4,1),(2,3),(3,2)) and no other non-diagonal pair, what can be said about symmetry?In which relation does the rule guarantee that if ((a,b)\in R), then ((b,a)\in R)?If (R) is not symmetric, what type of example is sufficient to prove it?If (A={1,2,3}) and (R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3)}), why is (R) not symmetric?On (A={1,2,3,4}), what type is (R={(a,b):a+b\text{ and }b+a\text{ are both equal to }6})?Which option gives the correct minimum correction for making the relation symmetric?If (R={(1,2),(2,1),(2,4),(4,2),(1,4)}), which pair must be added in the symmetric extension?What is the safest method to identify a symmetric relation?