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Class 12 · Mathematics
→On (A={1,2,3,4,5}), (R={(a,b):a-b\text{ is odd}}). Choose the correct statement about (R).
Class 12 · Mathematics
→On the set (A={1,2,3,4}), the relation (R={(a,b):a+b\text{ is even}}) is given. Is (R) reflexive?
Class 12 · Mathematics
→For a relation (R) on set (A), which condition is equivalent to reflexivity?
Class 12 · Mathematics
→On a non-empty set with (n) elements, what is the minimum number of pairs in a reflexive relation?
Class 12 · Mathematics
→On a four-element set, what is the maximum number of pairs a relation can have and still not be reflexive?
Class 12 · Mathematics
→For any family ({R_i}) of reflexive relations on the same set (A), what is (\bigcap R_i)?
Class 12 · Mathematics
→Can the union of two non-reflexive relations ever be reflexive?
Class 12 · Mathematics
→On (A={0,1,2}), (R={(a,b):a+b\text{ is divisible by }3}) is given. How many diagonal pairs must be added to make (R) reflexive?
Class 12 · Mathematics
→On integers, (R={(a,b):a \equiv b \pmod{3}}). What is correct about (R)?
Class 12 · Mathematics
→On real numbers, (R={(x,y):x-y>0}). Which statement is correct about (R)?
Class 12 · Mathematics
→On real numbers, (R={(x,y):x<y+1}). Is (R) reflexive?
Class 12 · Mathematics
→On real numbers, (R={(x,y):x-y\in \mathbb{Z}}) is given. Which statement about (R) is correct?
Class 12 · Mathematics
→If (f:A \to \mathbb{R}) and (R={(x,y):f(x)\le f(y)}), what is (R)?
Class 12 · Mathematics
→If (f:A \to \mathbb{R}) and (R={(x,y):f(x)<f(y)}), what is correct about (R)?
Class 12 · Mathematics
→If (f:A \to B) is a function and (R={(x,y):f(x)=f(y)}) on (A), which statement about (R) is correct?
Class 12 · Mathematics
→Which statement about equivalence relations and reflexive relations is correct?
Class 12 · Mathematics
→If a relation matrix has all off-diagonal entries (1), but one main diagonal entry is (0), what is the relation like?
Class 12 · Mathematics
→The matrix of a relation is (\begin{bmatrix}1&1&0\0&1&1\1&0&1\end{bmatrix}). Which statement about the relation is correct?
Class 12 · Mathematics
→Which matrix of a relation on a three-element set makes the relation reflexive?
Class 12 · Mathematics
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