Mathematics
Reflexive relation
Practice questions
If (A={2,3,4,5,6,8}) and (R={(a,b):\operatorname{lcm}(a,b)\text{ is less than or equal to }8}), how many diagonal pairs are in (R)?On (A={2,3,4,5,6,8}), (R={(a,b):\operatorname{lcm}(a,b)\text{ is less than }5}). How many pairs must be added to make (R) reflexive?If (A={1,2,3,4,5,6}) and (R={(a,b):a\mid b^2}), why is (R) reflexive?On (A={1,2,3,4,5,6}), (R={(a,b):a+1\mid b}). How many diagonal pairs are in (R)?If (A={1,2,3,4,5,6}) and (R={(a,b):a+1\mid b+1}), why is (R) reflexive?On (A={-3,-2,-1,0,1,2,3}), (R={(a,b):a^2+b^2\leq9}). How many diagonal pairs must be added to make (R) reflexive?If (A={-2,-1,0,1,2}) and (R={(a,b):ab\geq a+b}), how many diagonal pairs are in (R)?On (A={-2,-1,0,1,2}), (R={(a,b):ab\geq a+b}). How many pairs must be added to make (R) reflexive?If (A={1,2,3,4}) and (R={(a,b):(a-b)^2<1}), what is the correct conclusion about (R)?On (A={1,2,3,4}), (R={(a,b):(a-b)^2>0}). How many pairs must be added to make (R) reflexive?If (A={1,2,3,4,5}) and (R={(a,b):|a-b|\leq a-1}), how many diagonal pairs are in (R)?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?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?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)?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?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?If (A) has (5) elements, how many reflexive relations have exactly (12) ordered pairs?How many reflexive relations are possible on a set with six elements?If (A) has (n) elements, how many reflexive relations must contain one fixed non-diagonal pair ((p,q)), where (p\neq q)?On a four-element set, how many reflexive relations do not contain both ((1,2)) and ((2,1))?