Mathematics
Symmetric relation
Practice questions
On (A={1,2,3,4}), how many symmetric relations must contain both ((1,2)) and ((3,4))?On (A={1,2,3,4}), how many symmetric relations contain ((1,2)) but not ((2,1))?If (M) is the matrix of a relation (R), what is the correct matrix condition for (R) to be symmetric?On (A={1,2,3}), (R={(1,2),(2,3),(3,1)}). What is the minimum number of pairs to add to make (R) symmetric?On (A={1,2,3,4}), (R={(1,2),(2,1),(3,4)}). What must be done to make (R) symmetric?Which relation on (\mathbb{R}) is symmetric?Which statement gives the most accurate definition of a symmetric relation?If (R) and (S) are symmetric relations on (A), choose the correct statement about (R\triangle S), where (R\triangle S=(R-S)\cup(S-R)).On (A={1,2,3,4}), (R={(a,b):a\equiv -b \pmod{5}}). What is the correct statement about (R)?On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3)}). What is the minimum number of pairs to remove to make the relation symmetric?On the set (A={1,2,3,4,5}), the relation (R={(a,b):a+b\text{ is even}}) is given. Is (R) symmetric?On (A={1,2,3,4}), (R={(a,b):a-b\text{ is divisible by }2}). Choose the correct statement about (R).On (A={1,2,3}), (R={(1,2),(2,1),(2,3),(3,2),(1,1)}). Is (R) symmetric or not?On (A={a,b,c}), a symmetric relation contains ((a,b)) and ((c,a)). Which pairs must be present at minimum?How many symmetric relations can be formed on a set having three elements?For a set (A) with four elements, how many symmetric relations contain all diagonal pairs necessarily?If (A) has (n) elements, which is the total number of symmetric relations on (A)?On (A={1,2,3,4}), the matrix of a relation is (\begin{pmatrix}1&0&1&0\0&1&0&1\1&0&0&0\0&1&0&1\end{pmatrix}). What type is the relation?Which matrix represents a symmetric relation?If (R) is a symmetric relation on a set (A), which statement is true for (R^{-1})?