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Class 12 · Mathematics · Easy
→On (A={1,2}), (R={(1,1),(1,2)}) is given. Which pair must be added to make it symmetric?
Class 12 · Mathematics · Easy
→If a relation (R) contains ((4,7)) and (R) is symmetric, which ordered pair must definitely be in (R)?
Class 12 · Mathematics · Easy
→On the set (A={1,2,3}), the relation (R={(1,2),(2,1),(3,3)}) is given. What type of relation is it?
Class 12 · Mathematics · Expert
→On (A={1,2,3,4,5,6}), (R={(a,b):a-b\text{ is divisible by }7}). What fact proves that (R) is reflexive?
Class 12 · Mathematics · Expert
→If (A={1,2,3,4,5}) and (R={(a,b):a^2+b^2<2ab}), is (R) reflexive?
Class 12 · Mathematics · Expert
→On (A={0,1,2,3,4,5}), (R={(a,b):a^2+b^2=2ab}). Which statement about (R) is correct?
Class 12 · Mathematics · Expert
→If (A={0,1,2,3,4}) and (R={(a,b):a^2-a=b^2-b}), why is (R) reflexive?
Class 12 · Mathematics · Expert
→On (A={1,2,3,4,5}), (R={(a,b):a+b=ab}). How many pairs must be added to make (R) reflexive?
Class 12 · Mathematics · Expert
→If (A={1,2,3,4,5}) and (R={(a,b):a+b=ab}), how many diagonal pairs are in (R)?
Class 12 · Mathematics · Expert
→On (A={1,2,3,4,6,12}), (R={(a,b):a\mid b\text{ or }b\mid a}). What is the reason for (R) being reflexive?
Class 12 · Mathematics · Expert
→If (A={1,2,4,8,16}) and (R={(a,b):\frac{b}{a}\text{ is an integral power of }2}), why is (R) reflexive?
Class 12 · Mathematics · Expert
→On (A={2,3,4,5,6,7}), ((a,b)\in R) if (a) and (b) have a common prime factor. How many diagonal pairs are in (R)?
Class 12 · Mathematics · Expert
→If (A={1,2,3,4,5,6}) and ((a,b)\in R) only when (a) and (b) have a common prime factor, is (R) reflexive?
Class 12 · Mathematics · Expert
→On (A={\varnothing,{1},{2},{1,2}}), (R={(X,Y):X\subset Y\text{ or }X\cap Y=X}). What is the correct conclusion about (R)?
Class 12 · Mathematics · Expert
→If \(A=\mathcal{P}({1,2,3})) and (R={(X,Y):X\triangle Y\subseteq X}\), what is (R) with respect to reflexivity?
Class 12 · Mathematics · Expert
→On \(A=\mathcal{P}({1,2,3})\), \(R={(X,Y):X\setminus Y=X}\). How many diagonal pairs are in (R)?
Class 12 · Mathematics · Expert
→If \(S=\{1,2,3\}\) and \(A=\mathcal{P}(S)\), then a relation \(R\) on \(A\) is defined by \[R=\{(X,Y):X,Y\in A \text{ and } X\cup =S\}. \] How many diagonal pairs must be added to make \(R\) reflexive?
Class 12 · Mathematics · Expert
→For \(S={1,2,3}\) and \(A=\mathcal{P}(S)\), \(R={(X,Y):X\cup Y=Y}\). Is (R) reflexive?
Class 12 · Mathematics · Expert
→If (S={1,2,3}) and \(A=\mathcal{P}(S)\). On (A), (R={(X,Y):X\cap Y=X}). What is (R) with respect to reflexivity?
Class 12 · Mathematics · Expert
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