Mathematics
Reflexive relation
Practice questions
On (A={1,2,3,4}), (R={(a,b):a+b\text{ is divisible by }3}). Is (R) reflexive or not?On (A={1,2,3}), (R={(a,b):a+b\text{ is divisible by }2}). How many self-pairs will (R) contain?If (A={1,2,3}) and (R) is defined by (aRb) when (a=b) or (a+b=5), what is (R)?If (A={1,2,3}) and (R) is defined by (aRb) when (a\ne b) or (a=2), is (R) reflexive or not?On (A={1,2,3,4}), (R={(a,b):a\le b+1}). Is (R) reflexive?On (A={1,2,3,4}), (R={(a,b):a+1\le b}). What is correct about (R)?On (A={1,2,3}), (R={(a,b):ab>0}). Is (R) reflexive or not?On (A={-1,0,1}), (R={(a,b):ab>0}). Why is (R) not reflexive?On (A={1,2,3}), (R={(a,b):a+b\text{ is even}}) and (S={(a,b):a-b\text{ is even}}). Which statement about (R) and (S) is correct?If (A={1,2,3,4}) and (R) is a reflexive relation, what are the minimum and maximum possible numbers of pairs in (R)?On the set (A={1,2,3}), (R={(1,1),(2,2),(1,3),(3,1)}) is given. Which ordered pair must be added to make (R) reflexive?If (A={a,b,c,d}), what is the minimum number of ordered pairs that must be present in a reflexive relation on (A)?Which relation on (A={1,2,3}) is reflexive but not only the identity relation?If (A={1,2,3}) and (R={(a,b):a\le b}), why is (R) reflexive?On (A={1,2,3,4}), (R={(a,b):a-b\text{ is divisible by }2}). Is (R) reflexive?On (A={1,2,3,4}), (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 odd}}). What is the correct conclusion?If (A) has (5) elements, what is the total number of reflexive relations on (A)?If (A) has (n) elements, how many ordered pairs can be chosen freely in a reflexive relation?For the set (A={1,2,3}), the matrix of a relation is (\begin{bmatrix}1&0&1\0&1&0\1&0&0\end{bmatrix}). Is the relation reflexive?