Mathematics
Symmetric relation
Practice questions
On the set (A={1,2,3}), the relation (R={(1,1),(1,2),(2,1),(2,3),(3,2)}) is given. Why is this relation symmetric?On (A={1,2,3,4}), (R={(1,2),(2,1),(3,4)}). Which minimum pair must be added to make (R) symmetric?For a set A with n elements, how many unordered pair-positions must be chosen to specify a symmetric relation?How many symmetric relations are possible on the set (A={1,2,3,4})?For the relation (R={(1,2),(2,1),(2,3)}) on (A={1,2,3}), which statement is correct?If a relation (R) is symmetric and ((5,8) \in R), which conclusion is definitely true?A relation (R) on a set (A) is symmetric. Which statement about (R^{-1}) is correct?If (R={(a,b):a-b\text{ is even}}) is a relation on integers, what type is (R)?On natural numbers, (R={(a,b):a\leq b}) is given. Why is this relation not symmetric?On (A={1,2,3}), (R=\varnothing). Which statement is correct for (R)?For a set (A), which statement is correct about the universal relation (R=A\times A)?For the identity relation (I={(1,1),(2,2),(3,3)}) on (A={1,2,3}), what is the correct conclusion?If the matrix of a relation is (M=\begin{bmatrix}1&0&1\0&1&0\1&0&0\end{bmatrix}), which statement about the relation is correct?If the matrix of a relation is (M=\begin{bmatrix}1&1&0\0&1&1\0&1&1\end{bmatrix}), why is it not symmetric?What is the correct way to identify a symmetric relation in a directed graph?On (A={1,2,3,4}), (R={(a,b):a+b\text{ is even}}). Which statement about (R) is correct?On real numbers, (R={(a,b):a-b=3}) is given. What is the correct reason it is not symmetric?On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,3),(3,1)}). Which property is correct?If (R) and (S) are both symmetric relations on (A), which statement about (R\cap S) is correct?If (R) and (S) are both symmetric relations on (A), which statement about (R\cup S) is correct?