Mathematics
Transitive relation
Practice questions
On the set (A={1,2,3,4}), the relation (R={(a,b):a\le b}) is given. Why is this relation transitive?On (A={1,2,3}), (R={(1,2),(2,3),(1,3),(2,2)}). Which statement is correct?On (A={1,2,3,4}), the relation (R={(a,b):a\mid b}) is defined. Choose the correct option about (R).On (A={1,2,3}), (R={(1,2),(2,1),(1,1)}). Which minimum pair must be added to make it transitive?On real numbers, relation (R) is defined by (aRb) if (a-b) is rational. Choose the correct statement about transitivity of (R).On the integers, define aRb when a+b is even. Is R transitive?On (A={1,2,3,4,5}), (R={(a,b):|a-b|=1}). Which option is correct for (R)?On a set (A), the empty relation (R=\varnothing) is given. Is (R) transitive?On (A={1,2,3}), the universal relation (R=A\times A) is given. Which statement about (R) is correct?On natural numbers, (aRb) if (b=a+1). What is the correct conclusion about (R)?On real numbers, (aRb) if (a<b). Choose the correct reason for transitivity of (R).On (A={1,2,3,4}), (R={(1,2),(2,4),(1,4),(4,4)}). Which statement is correct?On (A={1,2,3}), (R={(1,2),(2,3)}). Which pair must be added in the transitive closure of (R)?On integers, (aRb) if (a-b) is divisible by (3). Choose the correct option about transitivity of (R).On (A={1,2,3,4}), (R={(a,b):a+b=5}). Is (R) transitive?If (R) and (S) are transitive relations on a set (A), which statement about (R\cap S) is always true?If (R) and (S) are transitive, which statement about (R\cup S) is correct?On (A={1,2,3,4}), (R={(a,b):a<b\text{ and }b-a\text{ is even}}). Choose the correct option for (R).On (A={1,2,3,4}), (R={(1,2),(2,4),(1,4),(2,2),(4,4)}). What is the correct conclusion about (R)?On integers, (aRb) if (a^2=b^2). Choose the correct option for transitivity of (R).