Mathematics
Symmetric relation
Practice questions
How many different symmetric relations can be formed on the set (A={1,2,3,4})?A set (A) has (5) elements. If every symmetric relation (R) must contain all diagonal pairs, how many such relations are possible?If (A={1,2,3}) and (R={(1,2),(2,1),(2,3)}), which minimum pair must be added to make (R) symmetric?On (A={1,2,3,4}), (R={(a,b):a+b\text{ is even}}) is given. Choose the correct statement about (R).On (A={1,2,3,4}), (R={(a,b):a-b\text{ is positive}}). Why is (R) not symmetric?If (R) and (S) are both symmetric relations on (A), which of the following relations is definitely symmetric?If (R) is a symmetric relation on (A), what is the correct statement about (R^{-1})?On a set with (4) elements, how many symmetric relations have exactly (3) diagonal pairs?On (A={1,2,3}), the matrix of relation (R) is (\begin{pmatrix}1&0&1\0&1&1\1&1&0\end{pmatrix}). What is the correct conclusion about (R)?On (A={1,2,3}), the matrix of relation (R) is (\begin{pmatrix}1&1&0\0&1&1\0&1&1\end{pmatrix}). Which minimum entry must be changed for symmetry?On (A={1,2,3,4}), (R={(a,b):|a-b|=1}). Choose the correct statement about (R).On (A={1,2,3,4,5}), (R={(a,b):a\equiv b \pmod{2}}). Why is (R) symmetric?On (A={1,2,3,4}), (R={(a,b):a\mid b}). Which is the correct counterexample showing that (R) is not symmetric?If A has n elements, how many symmetric relations on A contain no diagonal pair (a,a)?On (A={1,2,3}), how many symmetric relations must contain ((1,2))?On (A={1,2,3}), how many symmetric relations contain ((1,2)) but do not contain ((1,1))?If R is a symmetric relation, which statement about R ∪ R⁻¹ is correct?For any relation (R), what type of relation is (R\cup R^{-1}) always?On A = {1,2,3,4}, let R = {(a,b) : a + b = 5}. What type of relation is R?On (A={1,2,3,4}), (R={(a,b):a+b\text{ is odd}}). What is the correct statement about (R)?