Mathematics
Reflexive relation
Practice questions
If (A={1,2,3}), what fraction of all relations are reflexive relations?If (R) is a reflexive relation on (A={1,2,3}) with exactly 4 pairs, how many of those 4 pairs must be self-pairs?On (A={1,2,3}), how many reflexive relations with exactly 4 pairs are possible?On (A={1,2,3}), how many reflexive relations with exactly 5 pairs are possible?On (A={1,2,3,4}), what is the number of reflexive relations with exactly 6 pairs?On (A={1,2,3}), (R={(a,b):a^2=b^2}). Is (R) reflexive?On real numbers, (R={(a,b):a^2+b^2=0}). Is (R) reflexive?On (A={-1,0,1}), (R={(a,b):a^2=b^2}). Which statement is correct for (R)?On (A={1,2,3}), (R={(a,b):a+b=4}). Why is (R) not reflexive?On (A={1,2,3,4}), (R={(a,b):a+b\le 8}). Is (R) reflexive?On (A={1,2,3,4}), (R={(a,b):a+b<8}). (R) is not reflexive because which pair will be absent?On (A={1,2,3}), (R={(a,b):a) and (b) have the same parity(}). Why is (R) reflexive?On (A={1,2,3,4,5}), (R={(a,b):|a-b|) is even(}). Is (R) reflexive?On (A={1,2,3,4,5}), (R={(a,b):|a-b|) is odd(}). Why is (R) not reflexive?On (A={1,2,3}), (R={(a,b):a+b\ge 2}). Is (R) reflexive?On (A={1,2,3}), (R={(a,b):a+b>2}). (R) is not reflexive because which pair is missing?If (R) is reflexive on (A), which relation between the identity relation (I_A={(a,a):a\in A}) and (R) is correct?On (A={1,2,3}), (R={(1,1),(2,2),(1,2),(2,1),(3,1)}). Is (I_A\subseteq R) true?On (A={1,2,3,4}), (R) is reflexive and has 7 total pairs. What is the maximum number of non-diagonal pairs in (R)?On (A={1,2,3}), (R) is reflexive and ((1,2)\notin R). Which conclusion is correct?