Mathematics
Symmetric relation
Practice questions
If (R) is a symmetric relation, which statement about (R\setminus S) is always true?On (A={1,2,3}), (R={(1,2),(2,1),(2,3),(3,2)}). How many pairs must be added to make (R) both reflexive and symmetric?On (A={1,2,3,4}), (R={(1,2),(2,1),(2,4),(4,2),(3,4)}). How many minimum pairs must be added to make it symmetric?Which relation is definitely symmetric?Why is (R={(a,b):a\mid b}) on natural numbers not symmetric?In a symmetric relation on (A={1,2,3}), ((1,2)) and ((2,3)) are present. Which pairs must be present at minimum?If a relation (R) is symmetric, which of the following is not necessary?On real numbers, (R={(a,b):|a-b|<2}). What is correct about (R)?If (R={(a,b):a+b=10}) on real numbers, what type is (R)?If (R={(a,b):a=2b}) on real numbers, why is (R) not symmetric?How many symmetric relations on (A={1,2,3}) contain ((1,2))?How many symmetric relations on (A={1,2,3}) do not contain ((1,1))?A relation (R) on a set (A) is symmetric. If ((a,b)\notin R), which conclusion is always true?If (R) is symmetric and (S\subseteq R), which statement about (S) is correct?On (A={1,2,3,4}), (R={(a,b):a\equiv b \pmod{2}}). What is correct about (R)?If (R) is symmetric and (T=R\cup R^{-1}), which statement about (T) is correct?For any relation R, which statement about R ∪ R⁻¹ is always true?On (A={1,2,3}), (R={(1,2),(2,3)}). What is (R\cup R^{-1})?In the matrix of a symmetric relation, what is true about entries outside the main diagonal?If a relation matrix has (m_{24}=1) and (m_{42}=0), what can be said about the relation?