Mathematics
Reflexive relation
Practice questions
On real numbers, (R={(a,b):a^2+b^2\le k}). Which statement is correct about (R) being reflexive on all of (\mathbb{R})?On (A={-1,0,1}), (R={(a,b):a^2+b^2\le k}). What is the minimum value of (k) for (R) to be reflexive?On (A={1,2,3}), (R={(a,b):ab\ge k}). What is the maximum value of (k) for (R) to be reflexive?If (A) has (n) elements, what is the number of reflexive relations having exactly (n+2) pairs?On (A={1,2,3}), (R) is reflexive. If (R) contains ((1,2)) and ((2,3)), which pair must be in (R\circ R)?Let (A={1,2,3,4,5}) and (R={(a,b)\in A\times A:a+b\text{ is even}}). What is the minimum number of ordered pairs that must be added to make this relation reflexive?On (A={1,2,3,4,5}), (R={(a,b):a-b\text{ is divisible by }3}). Is (R) reflexive?If (A={0,1,2,3}) and (R={(a,b):a^2=b^2}), which statement about (R) is correct?On (A={1,2,3,4}), (R={(a,b):a<b}). How many pairs must be added to make (R) reflexive?If (A={1,2,3,4}) and (R={(a,b):a\leq b}), what type of relation is (R) with respect to reflexivity?On (A={2,4,6,8}), (R={(a,b):a\text{ divides }b}) is given. Why is (R) reflexive?If (A={1,2,3}) and (R={(1,1),(2,2),(1,2),(2,3)}), which pair must be added to make (R) reflexive?On (A={1,2,3,4}), (R={(a,b):|a-b|\leq 1}). Is (R) reflexive?On (A={1,2,3,4,5}), (R={(a,b):|a-b|<0}). What is (R) with respect to reflexivity?If (A={1,2,3,4}) and (R={(a,b):a+b\leq 6}), how many diagonal pairs must be added to make (R) reflexive?On (A={1,2,3,4,5}), (R={(a,b):a+b\geq 2a}). What is the correct reason that (R) is reflexive?If (A={1,2,3}) and (R=A\times A-{(2,2)}), choose the correct statement.A set (A) has (n) elements. How many relations on (A) are reflexive?How many reflexive relations are possible on a set (A) with three elements?On a set with four elements, how many relations are not reflexive?