Mathematics
Reflexive relation
Practice questions
On the set (A={1,2,3}), the relation (R={(1,1),(1,2),(2,2),(3,1)}) is given. Which pair must be added at minimum to make it reflexive?If a set (A) has (4) elements, how many reflexive relations can be formed on (A)?If (A) has (5) elements, how many reflexive relations have exactly (3) additional pairs apart from the diagonal pairs?On the set (A={p,q,r,s}), which of the following relations is definitely reflexive?The matrix of a relation on a three-element set is (\begin{bmatrix}1&0&1\1&0&0\0&1&1\end{bmatrix}). What is the minimum number of entries to change to make it reflexive?If (R) and (S) are reflexive relations on the same set (A), which statement about (R \cap S) is correct?If (R) is a reflexive relation on a set (A), which statement about (R^{-1}) is correct?What is the smallest necessary extension that makes a relation (R) reflexive?On (A={1,2,3,4}), (R={(a,b):a+b\text{ is even}}) is given. Which statement about (R) is correct?On (A={1,2,3,4,5}), (R={(a,b):a-b\text{ is divisible by }4}). Is (R) reflexive?On (A={1,2,3,4}), (R={(a,b):a+b\text{ is odd}}). What is the correct conclusion about (R)?On (A={2,4,6}), (R={(a,b):a \le b}). Why is (R) reflexive?On (A={2,4,6}), (R={(a,b):a<b}). Why is (R) not reflexive?On the power set (P(A)) of a set (A), the relation (R={(X,Y):X \subseteq Y}) is given. What is (R)?On (P(A)), (R={(X,Y):X \subset Y}), where (\subset) denotes proper subset. Which statement is correct about (R)?On (A={1,2,3,4}), (R={(a,b):a\text{ divides }b}). Which statement about (R) is correct?On (A={1,2,3}), (R={(a,b):\gcd(a,b)=1}) is given. Is (R) reflexive?On a set (A) of integers, (R={(a,b):a^2=b^2}) is given. Why is (R) reflexive?On (A={-1,0,1}), (R={(a,b):a+b=0}). Is (R) reflexive?On (A={1,3,5,7}), (R={(a,b):|a-b|\le 2}). Which statement about (R) is correct?