Mathematics
Symmetric relation
Practice questions
On the set (A={1,2,3}), the relation (R={(1,1),(2,2),(3,3),(1,2),(2,1)}) is given. What type of relation is it?If (A={1,2,3}) and (R={(1,2),(2,1),(2,3)}), which pair must be added to make (R) symmetric?On (A={1,2,3,4}), (R={(a,b):a+b\text{ is even}}). What can be said about this relation?On (A={1,2,3,4}), (R={(a,b):a-b\text{ is odd}}). Choose the correct statement about (R).In which relation is symmetry definitely present?If a relation (R) is symmetric and ((5,8)\in R), which pair must definitely belong to (R)?If (R) is symmetric, which of the following statements is always true?On (A={1,2,3}), (R={(1,2),(2,1),(1,3),(3,1),(2,2)}). Choose the correct option about (R).On (A={1,2,3}), why is the relation (R={(1,2),(2,1),(3,1)}) not symmetric?If (A) has 4 elements, how many symmetric relations can be formed on (A)?If (A) has (n) elements, what is the total number of symmetric relations on (A)?If (A={1,2}), how many symmetric relations are possible on (A)?Which option gives a relation that is not symmetric?If the matrix of a relation (R) is (\begin{pmatrix}1&0&1\0&1&0\1&0&1\end{pmatrix}), what is (R)?Which of the following matrices represents a symmetric relation?If R is symmetric, which statement about R⁻¹ is correct?If (R^{-1}=R), what is the correct conclusion about (R)?On (A={1,2,3,4}), (R={(a,b):|a-b|=1}). What is (R)?On (A={1,2,3,4}), (R={(a,b):a+2=b}). Choose the correct statement about (R).Which option gives a relation that is both symmetric and reflexive?