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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
→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
→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 set \(A\) has 5 elements, how many total relations are possible on \(A\)?
Class 11 · Mathematics
→If \(A=\{1,2,3,4\}\), \(B=\{3,4,5,6\}\), and \(R=\{(a,b)\in A\times B: b=a+2\}\), how many ordered pairs does \(R\) contain?
Class 11 · Mathematics
→On the set \(A=\{-2,-1,0,1,2,3\}\), define the relation \(R\) by \(aRb\) if and only if \(a\equiv b\pmod{3}\). What is the equivalence class \([-1]\)?
Class 11 · Mathematics
→A relation \(R=\{(a,b):a,b\in A\text{ and }a+b=6\}\) is defined on the set \(A=\{1,2,3,4,5\}\). How many ordered pairs does \(R\) contain?
Class 11 · Mathematics
→On the set \(A=\{2,3,4,6,8,12\}\), relation \(R\) is defined by \(aRb\) if and only if \(a\mid b\). If \((2,6)\in R\) and \((6,12)\in R\), which of the following pairs must belong to \(R\) by transitivity?
Class 11 · Mathematics
→On the set \(A=\{1,2,3,4,6,12\}\), a relation \(R\) is defined by \(aRb\) if and only if \(a\mid b\). Which of the following ordered pairs does not belong to \(R\)?
Class 11 · Mathematics
→On the set \(A=\{1,2,3,4\}\), let \(R=\{(a,b):a\leq b\}\). When the first element is \(4\), which set contains all the second elements related to it?
Class 11 · Mathematics
→How many equivalence classes are formed by the relation R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(3,4),(4,3)} defined on the set A={1,2,3,4}?
Class 11 · Mathematics
→Why is the relation \(R=\{(a,b)\in A\times A:a+b\ge 5\}\), defined on \(A=\{1,2,3,4\}\), not reflexive?
Class 11 · Mathematics
→On the set \(A=\{1,2,3,4,6,12\}\), a relation \(R\) is defined by \(aRb\) if and only if \(a\mid b\). How many first elements are related to \(12\)?
Class 11 · Mathematics
→If A = {1, 2} and B = {3, 4}, how many ordered pairs are there in A × B?
Class 11 · Mathematics
→If A = {1, 2} and B = {3, 4, 5}, how many elements are in A × B?
Class 11 · Mathematics
→If R = A × A on A = {1, 2, 3}, how many ordered pairs are in R?
Class 11 · Mathematics
→If a relation \(R=\{(a,b):a=b^2\}\) is defined on the set \(A=\{1,2,3,4\}\), which of the following is the correct form of \(R\)?
Class 11 · Mathematics
→If \(A=\{1,2,3,4\}\) and \(R\) is the relation consisting of ordered pairs for which \(a+b\) is odd, which of the following pairs belongs to \(R\)?
Class 11 · Mathematics
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