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Class 12 · Mathematics
→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
→On \(A=\mathcal{P}({1,2,3})\), \(R={(X,Y):X\setminus Y=X}\). How many diagonal pairs are in (R)?
Class 12 · Mathematics
→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
→For \(S={1,2,3}\) and \(A=\mathcal{P}(S)\), \(R={(X,Y):X\cup Y=Y}\). Is (R) reflexive?
Class 12 · Mathematics
→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
→If (S={1,2,3,4}) and (A=\mathcal{P}(S)), how many reflexive relations are possible on (A)?
Class 12 · Mathematics
→On (A={1,2,3,4,5}), a relation has exactly (18) pairs and is reflexive. How many pairs are present besides the compulsory diagonal pairs?
Class 12 · Mathematics
→If (A={1,2,3,4}), how many reflexive relations contain exactly (11) ordered pairs?
Class 12 · Mathematics
→On a five-element set, how many reflexive relations are neither the identity relation nor the universal relation?
Class 12 · Mathematics
→If (A={1,2,3,4}), how many reflexive relations have exactly (2) non-diagonal pairs and ((1,2)) is one of them?
Class 12 · Mathematics
→On a four-element set, how many reflexive relations do not contain both ((1,2)) and ((2,1))?
Class 12 · Mathematics
→If (A) has (n) elements, how many reflexive relations must contain one fixed non-diagonal pair ((p,q)), where (p\neq q)?
Class 12 · Mathematics
→How many reflexive relations are possible on a set with six elements?
Class 12 · Mathematics
→If (A) has (5) elements, how many reflexive relations have exactly (12) ordered pairs?
Class 12 · Mathematics
→On (A={1,2,3,4}), (R=A\times A-{(1,1),(2,3),(4,4)}). How many pairs must be added to make (R) reflexive?
Class 12 · Mathematics
→If (A={1,2,3,4,5,6}) and (R={(a,b):a=b\text{ and }a\equiv0 \pmod{2}}), how many pairs must be added to make (R) reflexive?
Class 12 · Mathematics
→On (A={1,2,3,4,5}), (R={(a,b):a\neq b\text{ and }a+b\text{ is even}}). Which statement is correct for (R)?
Class 12 · Mathematics
→If (A={1,2,3,4,5}) and (R={(a,b):a=b\text{ or }a+b\text{ is divisible by }3}), what is (R) with respect to reflexivity?
Class 12 · Mathematics
→On (A={0,1,2,3,4}), (R={(a,b):|a-b|\leq a-1}). How many pairs must be added to make (R) reflexive?
Class 12 · Mathematics
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