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Class 11 · Mathematics
→Is the union of two transitive relations always transitive? Choose the correct option.
Class 11 · Mathematics
→A relation R is defined on the set A={1,2,3,4} by R={(a,b): a-b∈{0,2,-2}}. Which of the following statements is correct?
Class 11 · Mathematics
→On (A={1,2,3,4,5}), (R={(a,b):|a-b|\le 1}). Which statement about (R) is correct?
Class 11 · Mathematics
→If \(A=\{1,2,3,4,5\}\) and \(R=\{(a,b)\in A\times A:a+b\le 6\}\), which statement is correct about \(R\)?
Class 11 · Mathematics
→On (A={1,2,3,4}), (R={(1,2),(2,3),(3,4)}). Which extra pairs will be in the transitive closure?
Class 11 · Mathematics
→On A = {1, 2, 3, 4, 5}, let R = {(1,2), (2,4), (4,5)}. What is the minimum number of pairs that must be added to make R transitive?
Class 11 · Mathematics
→On (A={2,3,4,6,9}), (R={(a,b):\gcd(a,b)>1}). Choose the correct statement.
Class 11 · Mathematics
→On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)}). Why is (R) not an equivalence relation?
Class 11 · Mathematics
→If a relation (R) is reflexive and antisymmetric, is it always transitive?
Class 11 · Mathematics
→On the set of integers, a relation R is defined by aRb if and only if \(a\leq b\). Which of the following properties is not true for this relation?
Class 11 · Mathematics
→On (A={1,2,3,4}), (R={(a,b):a=b \text{ or } |a-b|=1}). Choose the correct statement.
Class 11 · Mathematics
→If \(R=\{(x,y)\in\mathbb{R}^2:x-y>0\}\), what is the nature of \(R\)?
Class 11 · Mathematics
→On the set of real numbers, a relation R is defined by aRb if and only if a² = b². Which statement about this relation is correct?
Class 11 · Mathematics
→On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,3)}). Which pair must be added minimally to make (R) transitive?
Class 11 · Mathematics
→On (A={1,2,3,4}), (R={(a,b):a<b}). Which statement is correct?
Class 11 · Mathematics
→On the set A={1,2,3}, which pair must be added, at minimum, to make the relation R={(1,1),(2,2),(3,3),(1,2),(2,1)} an equivalence relation?
Class 11 · Mathematics
→For the relation \(R=\{(a,b):a\ne b\}\) on the set \(A=\{1,2,3\}\), choose the correct statement.
Class 11 · Mathematics
→On the set \(A=\{1,2,3,4,5\}\), let \(R=\{(a,b)\in A\times A:a+b\le 6\}\). Choose the correct statement.
Class 11 · Mathematics
→On the set \(A=\{1,2,3,4\}\), let \(R=\{(a,b)\in A\times A:a-b>0\}\). Which statement about this relation is correct?
Class 11 · Mathematics
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