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Class 11 · Mathematics
→If (A={1,2,3,4,5}) and (R={(a,b):a+b\equiv0\pmod{2}}), how many ordered pairs are in (R)?
Class 11 · Mathematics
→If (A={1,2,3,4}) and (R={(a,b):ab \text{ is even}}), which statement is correct for (R)?
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 (A=\mathbb{R}), (aRb) if and only if (a-b\geq0). Which relation is this?
Class 11 · Mathematics
→A relation R on the set of real numbers is defined by aRb if and only if |a| = |b|. What type of relation is R?
Class 11 · Mathematics
→On (A={1,2,3,4}), (R={(a,b):\operatorname{lcm}(a,b)=4}). Which pair belongs to (R)?
Class 11 · Mathematics
→On the set \(A=\{1,2,3,4,5,6\}\), the relation \(R=\{(a,b):\gcd(a,b)=1\}\) is defined. Choose the correct statement.
Class 11 · Mathematics
→If (A) has (n) elements, what is the number of antisymmetric relations on (A)?
Class 11 · Mathematics
→If A has n elements, what is the number of symmetric relations on A?
Class 11 · Mathematics
→If (A) has (n) elements, what is the formula for the number of reflexive relations on (A)?
Class 11 · Mathematics
→If (A) has (n) elements, what is the correct formula for the total number of relations on (A)?
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 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 (A={1,2,3,4}) and (R={(a,b):a=b \text{ or } a+b=5}), what is the correct statement about (R)?
Class 11 · Mathematics
→On a set (A), (R={(a,a):a\in A}) is the identity relation. Which property is correct?
Class 11 · Mathematics
→If (R) and (S) are reflexive relations on a set (A), then what type is (R\cap S)?
Class 11 · Mathematics
→If (R) and (S) are symmetric relations on a set (A), which statement about (R\cap S) is correct?
Class 11 · Mathematics
→On (A={1,2,3,4}), (R={(a,b):a+b \text{ is odd}}). What is the correct option for this relation?
Class 11 · Mathematics
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