Mathematics
Symmetric relation
Practice questions
Let (A={1,2,3,4}) and (R={(a,b):a+b\text{ is even}}). Choose the correct statement about relation (R).If a relation on (A={1,2,3}) is (R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3)}), which minimum pair must be added to make (R) symmetric?A set (A) has (n) elements. What is the total number of symmetric relations on (A)?On (A={1,2,3}), how many symmetric relations contain all reflexive pairs?If the matrix of a relation (R) is (M=\begin{pmatrix}1&0&1\0&1&0\1&0&0\end{pmatrix}), what can be said about (R)?On (A={1,2,3,4}), relation (R={(a,b):|a-b|=1}) is given. Choose the correct statement.On the set of real numbers, relation (R) is defined by (aRb) if ((a-b)^2=0). What is correct about (R)?If (R) and (S) are two symmetric relations on (A), which statement is always true?Which of the following relations on (A={1,2,3}) is symmetric but not transitive?If (R) is a symmetric relation, which statement about (R^{-1}) is correct?On (A={1,2,3,4}), relation (R={(a,b):a-b\text{ is divisible by }2}) is given. Choose the correct option for (R).A relation on (A={1,2,3}) has matrix (M). If (M) is not a symmetric matrix, which conclusion is definitely correct?If (R) is symmetric on (A) and (T\subseteq R), which statement about (T) is not always true?Which is the smallest symmetric relation on (A={1,2,3}) containing ((1,2)) and ((2,3))?A relation (R) on a set (A) is symmetric. If ((x,y)\notin R), which statement is definitely true?If (R) is a symmetric relation and it has (7) pairs in total, what is correct about the number of off-diagonal pairs?On (A={1,2,3,4}), relation (R={(a,b):a\cdot b\text{ is even}}) is defined. Choose the correct statement about (R).For any relation R, which statement about R∪R⁻¹ is always true?If (R) is symmetric, then (R\cap R^{-1}) is equal to which of the following?On (A={1,2,3}), how many symmetric relations contain exactly one diagonal pair?