Mathematics
Symmetric relation
Practice questions
On (A={1,2,3}), what must be done to make (R={(1,2),(2,1),(1,3)}) symmetric?On (A={1,2,3,4}), (R={(1,4),(4,1),(2,3),(3,2),(1,2)}). What is the minimum number of pairs to add to make it symmetric?On real numbers, relation (R) is defined by (aRb) if (|a|=|b|). What is correct about (R)?On a set (A), (R={(a,b):a\ne b}). Choose the correct statement about (R).On (A={1,2,3,4}), (R={(a,b):a+b\text{ is odd}}). Is (R) symmetric?On (A={1,2,3,4}), (R={(a,b):a<b}). Which statement is correct about (R)?On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1),(1,3)}). Which pair should be added to make (R) symmetric?What is the correct general form for the number of symmetric relations on an (n)-element set?If a relation (R) satisfies (R=R^{-1}), which conclusion is correct about (R)?On (A={1,2,3,4}), (R={(a,b):a^2+b^2=17}). What is (R)?On real numbers, (R={(a,b):a=2b}). Why is (R) not symmetric?On (A={1,2,3}), how many symmetric relations contain ((1,2)) and do not contain ((2,3))?On (A={1,2,3,4}), how many symmetric relations must contain all diagonal pairs ((a,a))?On (A={1,2,3,4}), how many symmetric relations contain no diagonal pair?On real numbers, (R={(a,b):(a-b)^2=4}). What type of relation is it?On (A={1,2,3,4,5}), (R={(a,b):a+b\le6}). Is (R) symmetric?On (A={1,2,3,4,5}), (R={(a,b):a+2b=6}). What is correct about (R)?A relation (R) on a set (A) is symmetric and (S\subseteq R). Must (S) be symmetric?On (A={1,2,3}), (R={(1,2),(2,1)}) and (S={(2,3),(3,2)}). What is (R\cup S)?On (A={1,2,3,4}), (R={(1,2),(2,1),(2,4),(4,2),(3,3)}). Choose the correct statement about (R^{-1}).