Mathematics
Reflexive relation
Practice questions
On A = {1, 2, 3}, let R = {(a, b) : a² = b²}. Is R reflexive?On (A={1,2,3}), (R={(a,b):a^2<b^2}). Is (R) reflexive?On (A={1,2,3,4}), (R={(a,b):a\equiv b \pmod{2}}). Which statement about (R) is correct?On (A={1,2,3,4,5}), (R={(a,b):a-b\equiv 0 \pmod{3}}). Is (R) reflexive?On (A={1,2,3}), (R={(a,b):a+b\equiv 0 \pmod{2}}). Why is (R) reflexive?On (A={1,2,3}), (R={(a,b):a+b\equiv 1 \pmod{2}}). What is (R)?If (R) is reflexive on (A) and (I_A) is the identity relation on (A), which statement is correct?If R and S are two reflexive relations on A, what can be said about R ∩ S?If (R) and (S) are two reflexive relations on (A), which statement about (R\cup S) is correct?If (R) is reflexive on (A), what is correct about (R^{-1})?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)?On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2)}). Will (R^{-1}) be reflexive?If (A=\varnothing), which statement is correct about the empty relation on (A)?If (A\ne\varnothing), why is the empty relation (R=\varnothing) on (A) not reflexive?On A = {1, 2, 3}, let R = (A × A) \ {(2, 2)}. Which statement about R is correct?On A = {1, 2, 3}, let R = (A × A) \ {(1, 2), (2, 3)}. What is R?If (R) is reflexive on (A), how many pairs of the identity relation must be contained in (R) when (|A|=6)?On (A={1,2,3}), the relation (R) contains only ((1,1),(2,2),(3,3),(1,3),(3,1)). Which statement is correct?Which option gives the best symbolic identification of a reflexive relation?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?