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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
→If (R={(a,b):a\ne b}) on (A={1,2,3,4}), choose the correct statement.
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={-2,-1,1,2}) and (R={(a,b):a^2=b^2}), what is the equivalence class ([-2])?
Class 12 · Mathematics
→On A = {1,2,3,4}, let R = {(a,b) : a^2 = b^2}. What type of relation is R?
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={1,2,3,4,6,12}), (aRb) means (a\mid b). Due to transitivity, which pair must follow from ((2,6)) and ((6,12))?
Class 11 · Mathematics
→If (A={1,2,3,4}) and (R={(1,1),(2,2),(3,3),(4,4),(1,3),(3,1)}), which statement about (R) is correct?
Class 11 · Mathematics
→On (A={1,2,3,4}), (R={(a,b):a+b \text{ is odd}}). Which property fails for (R)?
Class 11 · Mathematics
→If A has 3 elements, how many relations on A are both reflexive and symmetric?
Class 11 · Mathematics
→If (A={1,2,3,4}) and (R={(a,b):|a-b|=1}), which property is true?
Class 11 · Mathematics
→For the universal relation (A\times A) on (A={1,2,3}), which statement is correct?
Class 11 · Mathematics
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