Mathematics
Reflexive relation
Practice questions
If (A={1,2,3,4}) and a relation (R) is reflexive with exactly (10) ordered pairs, how many pairs in (R) are other than the compulsory diagonal pairs?On (A={1,2,3,4}), how many reflexive relations have exactly (10) ordered pairs?If (A={1,2,3,4,5}), how many reflexive relations have exactly (9) ordered pairs?In how many ways can a reflexive relation with exactly (5) ordered pairs be formed on (A={1,2,3})?If (A={1,2,3,4}) and (R) is reflexive, what is the minimum possible number of ordered pairs in (R)?On (A={1,2,3,4,5}), a relation (R) contains all non-diagonal pairs but no diagonal pair. How many pairs must be added to make (R) reflexive?If (A={1,2,3,4}) and (R={(a,b):a+b\text{ is odd}}), which statement is correct about (R)?On (A={1,2,3,4,5,6}), (R={(a,b):a\equiv b \pmod{2}}). Is (R) reflexive?On (A={1,2,3,4,5,6}), (R={(a,b):a\equiv b+1 \pmod{2}}). What is the correct conclusion about (R)?If (A={1,2,3,4,5}) and (R={(a,b):a^2\equiv b^2 \pmod{3}}), why is (R) reflexive?On (A={1,2,3,4}), (R={(a,b):a^2+b^2\text{ is even}}). Is (R) reflexive?If (A={1,2,3,4}) and (R={(a,b):a^2-b^2\text{ is odd}}), what is (R) with respect to reflexivity?On (A={1,2,3,4,5}), (R={(a,b):a+b=2a}). Which statement about (R) is correct?If (A={1,2,3,4}) and (R={(a,b):a+b=5}), how many pairs must be added to make (R) reflexive?On (A={1,2,3,4,5}), (R={(a,b):a+b=6}). How many diagonal pairs are already in (R)?If (A={1,2,3,4,5}) and (R={(a,b):a+b=6}), how many pairs must be added to make (R) reflexive?On (A={0,1,2,3}), (R={(a,b):ab=0\Rightarrow a=b}). Is (R) reflexive?If (A={0,1,2}) and (R={(a,b):ab>0}), how many pairs must be added to make (R) reflexive?On (A={-1,0,1}), (R={(a,b):ab\geq0}). Is (R) reflexive?If (A={-2,-1,0,1,2}) and (R={(a,b):a+b>0}), how many diagonal pairs are in (R)?