Mathematics
Reflexive relation
Practice questions
On (A={-2,-1,0,1,2}), (R={(a,b):a+b>0}). How many pairs must be added to make (R) reflexive?If (A={1,2,3,4}) and (R={(a,b):\min(a,b)=a}), what is (R) with respect to reflexivity?On (A={1,2,3,4}), (R={(a,b):\max(a,b)=b}). Which conclusion is correct?If (A={1,2,3,4,5}) and (R={(a,b):\gcd(a,b)=a}), is (R) reflexive?If (A={1,2,3,4,5}) and (R={(a,b):\gcd(a,b)=1}), how many pairs must be added to make (R) reflexive?On (A={1,2,3,4,5,6}), (R={(a,b):\operatorname{lcm}(a,b)=a}). Why is (R) reflexive?On (A={{1},{2},{1,2}}), relation (R) is defined by (XRY) if (X\subseteq Y). Is (R) reflexive?On (A={{1},{2},{1,2}}), (XRY) if (X\subset Y). What is (R) with respect to reflexivity?If (S={1,2,3}) and (A=\mathcal{P}(S)). On (A), (R={(X,Y):X\cap Y=X}). Is (R) reflexive?If (S={1,2}) and (A=\mathcal{P}(S)). On (A), (R={(X,Y):X\cup Y=S}). How many diagonal pairs must be added to make (R) reflexive?If (S={1,2,3}) and (A=\mathcal{P}(S)). On (A), (R={(X,Y):X\triangle Y=\varnothing}). Choose the correct statement about (R).On (A={1,2,3,4}), relation (R) is defined by ((a,b)\in R) if (a) and (b) have a common prime factor. Is (R) reflexive?If (A={2,3,4,5,6}) and ((a,b)\in R) if (a) and (b) have a common prime factor, which statement about (R) is correct?On (A={1,2,3,4}), (R) is defined as ((a,b)\in R) if (a=b) or (a+b=5). Is (R) reflexive?If (A={1,2,3,4}) and (R={(a,b):a=b\text{ and }a+b\text{ is even}}), what is the correct conclusion about (R)?If (A={1,2,3,4}) and (P={(1,3),(3,1),(2,2)}), how many reflexive relations (R) on (A) satisfy (P\subseteq R)?If (A) has 6 elements, what is the number of reflexive relations on (A) having exactly 9 pairs?On (A={1,2,3,4}), how many reflexive relations are not the identity relation but may be the universal relation?On (A={1,2,3,4}), how many reflexive relations have at most 6 pairs?On (A={1,2,3}), how many reflexive relations contain exactly one of ((1,2)), ((2,3)), and ((3,1))?