Mathematics
Reflexive relation
Practice questions
If (A={1,2,3,4,5,6}) and (R={(a,b):|a-b|\text{ is even}}), why is (R) reflexive?On (A={1,2,3,4}), (R={(a,b):a+b\text{ is even and }a\neq b}). 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 odd}}), what is (R) with respect to reflexivity?On (A={1,2,3,4,5}), (R={(a,b):a=b\text{ and }a+b\text{ is odd}}). Is (R) reflexive?If (A={1,2,3,4}) and (R={(a,b):a\neq b\text{ or }a+b\text{ is even}}), what is the correct conclusion about (R)?On (A={1,2,3}), relation (R) contains all pairs of (A\times A) except ((1,1)) and ((2,2)). How many pairs must be added to make (R) reflexive?How many reflexive relations with exactly (7) ordered pairs are possible on a four-element set (A)?On a five-element set, how many reflexive relations have exactly (6) more pairs than the minimum possible number?If (A) has (n) elements, how many reflexive relations have exactly (n+2) ordered pairs?On a three-element set, how many relations are reflexive but not the universal relation?On a four-element set, how many relations are reflexive and different from the identity relation?If (A={1,2,3,4}), how many reflexive relations must contain ((1,2)) and must not contain ((2,1))?On a three-element set, how many reflexive relations contain at least one non-diagonal pair?On (A={1,2,3,4}), (R) is reflexive and has exactly (9) pairs. How many such relations are possible?If (A={1,2,3,4,5}), how many reflexive relations have no non-diagonal pair?On (A={1,2,3,4}), (R) is a relation containing every ((a,a)) and missing exactly two non-diagonal pairs. How many total pairs does (R) have?If (S={1,2,3}) and (A=\mathcal{P}(S)). On (A), (R={(X,Y):X\subseteq Y}). How many diagonal pairs are in (R)?If (S={1,2,3}) and (A=\mathcal{P}(S)). (R={(X,Y):X\cap Y=\varnothing}). How many diagonal pairs must be added to make (R) reflexive?For (S={1,2,3}) and (A=\mathcal{P}(S)), (R={(X,Y):X\cup Y=X}). Is (R) reflexive?If (S={1,2}) and (A=\mathcal{P}(S)). (R={(X,Y):X\setminus Y=\varnothing}). Which statement about (R) is correct?