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Class 12 · Mathematics · Hard
→On integers, the relation (R={(a,b):a-b=3}) is given. Why is it not symmetric?
Class 12 · Mathematics · Hard
→For the relation (R={(a,b):a^2=b^2}) on the set of real numbers, what is the correct statement?
Class 12 · Mathematics · Hard
→If (A={1,2,3}) and (R={(1,1),(2,2),(3,3),(1,2),(2,1),(1,3)}), (R) is not symmetric because which pair is missing?
Class 12 · Mathematics · Hard
→If (R) and (S) are two symmetric relations on (A), choose the correct statement about (R\cup S).
Class 12 · Mathematics · Hard
→If (R) and (S) are two symmetric relations on (A), what is true about (R\cap S)?
Class 12 · Mathematics · Hard
→For the relation (R={(x,y):x-y\text{ is odd}}), where (x,y\in {1,2,3,4}), which statement is correct?
Class 12 · Mathematics · Hard
→If (A={1,2,3}) and (R={(1,2),(2,1),(2,3),(3,2)}), choose the correct statement about (R).
Class 12 · Mathematics · Hard
→If (R) is a symmetric relation and ((5,8) \in R), which pair must definitely belong to (R)?
Class 12 · Mathematics · Hard
→If the matrix of a relation is (M=\begin{bmatrix}1&0&1\0&1&0\1&0&0\end{bmatrix}), what is the correct statement about the relation?
Class 12 · Mathematics · Hard
→What is the number of symmetric relations on the set (A={1,2,3,4})?
Class 12 · Mathematics · Hard
→If (A={1,2,3,4}) and (R={(a,b):a\le b}), why is (R) not symmetric?
Class 12 · Mathematics · Hard
→If (A={1,2,3}) and (R={(a,b):a+b\text{ is even}}), choose the correct statement about (R).
Class 12 · Mathematics · Hard
→How many symmetric relations can be formed on A={1,2,3}?
Class 12 · Mathematics · Hard
→If (A={1,2,3,4}) and (R={(1,1),(2,2),(3,3),(4,4),(1,3),(3,1),(2,4)}), which ordered pair must be added at minimum to make (R) symmetric?
Class 12 · Mathematics · Hard
→If (A={1,2,3}) and (R={(1,1),(2,2),(1,2),(2,1),(2,3),(3,2)}), which property does (R) definitely have?
Class 12 · Mathematics · Hard
→On (A={1,2,3,4}), how many symmetric relations must contain ((1,2)) and must not contain ((3,4))?
Class 12 · Mathematics · Hard
→Which statement is true for a symmetric relation but generally not true for an antisymmetric relation?
Class 12 · Mathematics · Hard
→If a relation (R) contains ((1,2),(2,1),(2,3),(3,2),(1,3)) and no other off-diagonal pair, what is necessary for symmetry?
Class 12 · Mathematics · Hard
→On (A={1,2,3,4}), relation (R={(a,b):a+b=5}) is defined. Is (R) symmetric?
Class 12 · Mathematics · Hard
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