Mathematics
Transitive relation
Practice questions
Which statement is true about (R={(1,2),(3,4)})?In a transitive relation, ((x,y)) and ((y,z)) are present. Which symbolic conclusion is correct?On (A={a,b,c}), (R={(a,b),(b,c),(a,c),(c,c)}). Is it transitive?On (A={a,b,c}), (R={(a,b),(b,c),(c,a)}). Is (R) transitive?If (R) is transitive and ((1,2)), ((2,3)), ((1,3)) are all in (R), which conclusion is not necessary?In which relation does the transitivity condition directly appear satisfied?If ((2,2)\in R) and ((2,5)\in R), which pair is needed for transitivity?If ((4,6)\in R) and ((6,6)\in R), which pair does transitivity require?Relation (R) is transitive. If (aRb) and (bRc), which statement is correct?What is the first useful thing to check while testing transitivity?A relation (R) on a set (A) is called transitive when which condition is true for all (a,b,c \in A)?On (A={1,2,3}), (R={(1,2),(2,3),(1,3)}) is given. What is the nature of this relation?On A={1,2,3}, let R={(1,2),(2,3)}. Why is R not transitive?The relation (R={(1,1),(1,2),(2,2)}) is given on (A={1,2}). Is (R) transitive?On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,3)}). Which pair must be added to make (R) transitive?On the set of natural numbers, define (aRb) if (a) divides (b). What kind of relation is this?On real numbers, define (aRb) if (a \le b). Is (R) transitive?On real numbers, define (aRb) if (a<b). Why is this relation transitive?On integers, define (aRb) if (a-b) is even. Is (R) transitive?On integers, (aRb) if (a-b) is odd. Is this relation transitive?