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Class 11 · Mathematics
→If (A={1,2,3,4,5}) and (R={(a,b):a+b \text{ is prime}}), which statement about (R) is correct?
Class 11 · Mathematics
→On (A={2,3,4,6}), (R={(a,b):\operatorname{lcm}(a,b)=12}). Which property is true?
Class 11 · Mathematics
→If A={1,2,3,4} and R={(a,b)∈A×A : ab is even}, which statement about R is correct?
Class 11 · Mathematics
→On the set \(A=\{1,2,3,4\}\), let \(R=\{(a,b):a\ge b\}\). Which statement about the relation \(R\) is correct?
Class 11 · Mathematics
→If \(A=\{1,2,3\}\) and \(R=\{(1,1),(2,2),(3,3),(1,2),(2,3)\}\), which single ordered pair must be added to make \(R\) transitive?
Class 11 · Mathematics
→Is the union of two transitive relations always transitive? Choose the correct option.
Class 11 · Mathematics
→If (R) and (S) are symmetric relations, which statement is always true about (R\cup S)?
Class 11 · Mathematics
→If (R) and (S) are two reflexive relations on (A), which statement is always true about (R\cap S)?
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
→If an equivalence relation \(R\) defined on the set \(A=\{1,2,3,4\}\) has equivalence classes \(\{1,4\}\) and \(\{2,3\}\), how many ordered pairs does \(R\) contain?
Class 11 · Mathematics
→Which option gives a partition of (A={1,2,3})?
Class 11 · Mathematics
→On (A={1,2,3}), (R={(1,1),(1,2),(2,1),(2,2),(3,3)}). What are its equivalence classes?
Class 11 · Mathematics
→If (A={1,2,3,4,5}) and (R={(a,b):a+b>7}), how many ordered pairs are in (R)?
Class 11 · Mathematics
→A relation R is defined on the set A = {1, 2, 3, 4} by R = {(a, b) : a + b = 6}, where a, b ∈ A. How many ordered pairs does R contain?
Class 11 · Mathematics
→If \(R=\{(1,2),(2,3),(1,3)\}\) and \(S=\{(2,1),(3,2),(3,1)\}\), what is \(S\) in relation to \(R\)?
Class 11 · Mathematics
→For which type of relation is the inverse relation equal to the relation itself, that is, \(R^{-1}=R\)?
Class 11 · Mathematics
→On the set \(A=\{1,2,3,4\}\), define the relation \(R=\{(a,b)\in A\times A: a+b\text{ is even}\}\). What is the equivalence class \([1]\) under this relation?
Class 11 · Mathematics
→If (A={1,2,3}), how many reflexive relations on (A) do not include ((1,2))?
Class 11 · Mathematics
→On (A={1,2,3,4,5,6}), (R={(a,b):\gcd(a,b)=1}). Which property is necessarily true?
Class 11 · Mathematics
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