Mathematics
Reflexive relation
Practice questions
On real numbers, (R={(x,y):x-y\in \mathbb{Z}}) is given. Which statement about (R) is correct?On real numbers, (R={(x,y):x<y+1}). Is (R) reflexive?On real numbers, (R={(x,y):x-y>0}). Which statement is correct about (R)?On integers, (R={(a,b):a \equiv b \pmod{3}}). What is correct about (R)?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?Can the union of two non-reflexive relations ever be reflexive?For any family ({R_i}) of reflexive relations on the same set (A), what is (\bigcap R_i)?On a four-element set, what is the maximum number of pairs a relation can have and still not be reflexive?On a non-empty set with (n) elements, what is the minimum number of pairs in a reflexive relation?For a relation (R) on set (A), which condition is equivalent to reflexivity?On the set (A={1,2,3,4}), the relation (R={(a,b):a+b\text{ is even}}) is given. Is (R) reflexive?On (A={1,2,3,4,5}), (R={(a,b):a-b\text{ is odd}}). Choose the correct statement about (R).If (A={2,3,5,7}) and (R={(a,b):a\text{ divides }b}), how many minimum pairs must be added to make (R) reflexive?On (A={1,2,3,4}), (R={(a,b):a<b}). Which set of pairs must be added to make (R) reflexive?If (A={1,2,3}) and (R={(1,1),(2,2),(1,2),(2,3),(3,1)}), which pair must be added to make (R) reflexive?On (A={1,2,3,4}), (R={(a,b):a+b\geq 2a}) is given. Is (R) reflexive?On (A={1,2,3,4,5}), (R={(a,b):|a-b|<1}). Which option is correct for (R)?If (A={1,2,3,4}) and (R={(a,b):|a-b|\leq 0}), what is (R)?On (A={0,1,2,3}), the relation (R={(a,b):a^2=b^2}) is given. Is (R) reflexive?On (A={-2,-1,0,1,2}), (R={(a,b):a^2=b^2}). What is the main reason (R) is reflexive?