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Class 12 · Mathematics
→On (A={1,2,3,4}), (R={(a,b):a+b\text{ is even}}) is given. Which statement about (R) is correct?
Class 12 · Mathematics
→What is the smallest necessary extension that makes a relation (R) reflexive?
Class 12 · Mathematics
→If (R) is a reflexive relation on a set (A), which statement about (R^{-1}) is correct?
Class 12 · Mathematics
→If (R) and (S) are reflexive relations on the same set (A), which statement about (R \cap S) is correct?
Class 12 · Mathematics
→The matrix of a relation on a three-element set is (\begin{bmatrix}1&0&1\1&0&0\0&1&1\end{bmatrix}). What is the minimum number of entries to change to make it reflexive?
Class 12 · Mathematics
→On the set (A={p,q,r,s}), which of the following relations is definitely reflexive?
Class 12 · Mathematics
→If (A) has (5) elements, how many reflexive relations have exactly (3) additional pairs apart from the diagonal pairs?
Class 12 · Mathematics
→If a set (A) has (4) elements, how many reflexive relations can be formed on (A)?
Class 12 · Mathematics
→On the set (A={1,2,3}), the relation (R={(1,1),(1,2),(2,2),(3,1)}) is given. Which pair must be added at minimum to make it reflexive?
Class 12 · Mathematics
→A student says that a relation on (A={1,2,3}) is reflexive because it contains ((1,1)) and ((2,2)). What missing point should the teacher mention?
Class 12 · Mathematics
→Which option gives the best symbolic identification of a reflexive relation?
Class 12 · Mathematics
→On (A={1,2,3}), the relation (R) contains only ((1,1),(2,2),(3,3),(1,3),(3,1)). Which statement is correct?
Class 12 · Mathematics
→If (R) is reflexive on (A), how many pairs of the identity relation must be contained in (R) when (|A|=6)?
Class 12 · Mathematics
→On A = {1, 2, 3}, let R = (A × A) \ {(1, 2), (2, 3)}. What is R?
Class 12 · Mathematics
→On A = {1, 2, 3}, let R = (A × A) \ {(2, 2)}. Which statement about R is correct?
Class 12 · Mathematics
→If (A\ne\varnothing), why is the empty relation (R=\varnothing) on (A) not reflexive?
Class 12 · Mathematics
→If (A=\varnothing), which statement is correct about the empty relation on (A)?
Class 12 · Mathematics
→On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2)}). Will (R^{-1}) be reflexive?
Class 12 · Mathematics
→On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2)}) and (S={(1,1),(2,2),(3,3),(2,3)}). What is (R\cap S)?
Class 12 · Mathematics
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