Mathematics
Reflexive relation
Practice questions
If (R) is not reflexive, what can be the simplest reason?On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,3),(3,1)}). Why is (R) reflexive?Choose the correct statement about the identity relation (I_A) on a set (A).If (A={1,2,3}) and (R) has only ((1,1)) and ((2,2)) as self-pairs, which statement is correct for (R)?On (A={1,2,3,4}), (R={(a,b):a-b\text{ is even}}). Is (R) reflexive or not?On (A={1,2,3}), (R={(a,b):a-b\text{ is odd}}). Which statement is correct?On (A={1,2,3}), (R={(a,b):a\ge b}). Is (R) reflexive?On (A={1,2,3}), (R={(a,b):a>b}). Why is (R) not reflexive?On (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,4)}). Choose the correct answer about (R).How many pairs are there in the smallest reflexive relation on a set with (n) elements?How many pairs are there in the universal relation on a set with (n) elements?Which relation is not reflexive on (A={1,2})?On (A={1,2,3}), (R={(a,b):a=b\text{ or }a=1}). Is (R) reflexive?On (A={1,2,3}), (R={(a,b):a\ne b}). What is correct about (R)?If (R) is reflexive and (A={4,5,6}), which statement is always true?On (A={1,2,3}), if one pair is added to (R={(1,1),(2,2),(3,3)}), which added pair will still keep (R) reflexive?On (A={1,2,3}), what must be done to make (R={(1,1),(2,2),(1,3),(3,2)}) reflexive?In a reflexive relation (R) on (A={1,2,3,4}), how many self-pairs will be there at minimum?A relation contains ((a,a)) for all (a\in A), but some ((a,b)) pairs are missing. Can the relation be reflexive?On (A={1,2,3}), (R) is reflexive and (S) contains all pairs of (R). If (S) is also a relation on (A), what can be said about (S)?