Mathematics
Symmetric relation
Practice questions
If (R) is a symmetric relation on a set (A), which statement about (R^{-1}) is correct?How many symmetric relations can be formed on the set (A={1,2,3})?If a set (A) has (4) elements, what is the total number of symmetric relations on (A)?On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1)}). Choose the correct statement about this relation.Which relation needs no new pair to be added in order to be symmetric?On (A={1,2,3,4}), (R={(a,b):a+b\leq5}). Is (R) symmetric?On (A={1,2,3,4}), (R={(a,b):a+b\text{ is odd}}). What can be said about (R)?On (A={1,2,3,4}), (R={(a,b):a=2b}). Which statement is correct about (R)?If (R) and (S) are both symmetric relations on a set (A), which statement about (R\cap S) is correct?If R and S are both symmetric relations, what is the correct statement about R ∪ S?On (A={1,2,3}), which relation is not symmetric?Why is the empty relation (\varnothing) considered symmetric on any set (A)?Why is the universal relation (A\times A) symmetric on any set (A)?On (A={1,2,3}), how many pairs must be added to (R={(1,2),(2,1),(1,3)}) to make it symmetric?Which condition definitely gives a symmetric relation?On (A={-1,0,1}), (R={(a,b):a^2=b^2}). What type is (R) with respect to symmetry?On (A={1,2,3,4,5}), (R={(a,b):|a-b|\leq2}). Choose the correct statement about (R).On (A={1,2,3,4}), (R={(a,b):a+b\equiv 0 \pmod{3}}). Is (R) symmetric?On (A={1,2,3,4}), (R={(a,b):a-b\equiv 0 \pmod{3}}). What can be said about (R)?On (A={1,2,3,4}), (R={(a,b):a-b\equiv 1 \pmod{3}}). Is (R) symmetric?