Mathematics
Reflexive relation
Practice questions
Which option gives only the necessary reflexive pairs on (A={1,2,3})?For a reflexive relation (R), what is always true when (a\in A)?On (A={0,1,2}), (R={(0,0),(1,1),(2,2),(0,1)}). Is (R) reflexive?On (A={0,1,2}), (R={(1,1),(2,2)}). Which pair should be added to make (R) reflexive?If a relation on (A={1,2,3,4}) has only ((1,1),(2,2),(3,3),(4,4)), what is it called?Which relation on (A={1,2,3}) is both reflexive and the identity relation?If a relation is not reflexive, what is the most direct possible reason?On (A={1,2,3}), (R={(a,b):a=b\text{ or }a<b}). Is (R) reflexive?On (A={1,2,3}), (R={(a,b):a\ne b}). Is (R) reflexive?In class, a teacher says that every element must be related to itself. This identifies which type of relation?If (A={1,2,3}), how many reflexive relations can be formed on (A)?If a set (A) has 4 elements, what is the number of reflexive relations on (A)?If (A) has (n) elements, which is the number of reflexive relations on (A)?On (A={1,2,3,4}), (R={(1,1),(2,2),(4,4),(1,3),(3,2)}). What is the minimum number of pairs needed to make (R) reflexive?Let (A={a,b,c,d}) and (R={(a,a),(c,c),(a,b),(d,c)}). (R) is not reflexive because which self-pairs are missing?On (A={1,2,3}), (R={(a,b):a\le b}). Why does (R) satisfy reflexivity?On (A={1,2,3}), (R={(a,b):a<b}). Which required pair will not be formed in (R)?On integers, (R={(a,b):a-b) is divisible by (3)(}). Is (R) reflexive?On integers, (R={(a,b):a+b) is odd(}). Why is (R) not reflexive?On (A={1,2,3,4}), (R={(a,b):a \equiv b \pmod{2}}). Reflexivity of (R) is based on which fact?