Mathematics
Symmetric relation
Practice questions
Which statement is correct about the identity relation (I_A={(a,a):a\in A})?If (R) is symmetric and ((p,q)\notin R), which conclusion is always correct?If (R) is symmetric and ((q,p)\notin R), what conclusion is correct about ((p,q))?Which condition most clearly gives a symmetric relation?On (A={1,2,3,4,5}), (R={(a,b):a+b=6}). How many pairs are in (R), and is it symmetric?On (A={1,2,3,4}), (R={(a,b):a+b\text{ is odd}}). How many ordered pairs are in (R)?For the same relation (R={(a,b):a+b\text{ is odd}}) on (A={1,2,3,4}), which statement is correct?For (R={(a,b):a+b\text{ is even}}) on (A={1,2,3,4}), which statement is correct?Which example is symmetric but not transitive?If the directed graph of a relation shows a reverse arrow for every arrow, what type of relation is it?A directed graph has arrows (1\to2), (2\to1), (2\to3), and no other arrows. What must be added to make it symmetric?If (A) has (4) elements, how many symmetric relations are not reflexive?How many symmetric relations are there on a set with (5) elements?In which relation is (R) symmetric but not reflexive?If (R) is a symmetric relation, what is (R\cap R^{-1}) equal to?If (R) is a symmetric relation, what is (R\cup R^{-1}) equal to?On (A={1,2,3,4}), (R={(a,b):a^2+b^2\text{ is even}}). Which statement is correct about (R)?On (A={1,2,3,4}), (R={(a,b):a+2b\text{ is even}}). Is (R) symmetric?When will the relation (R={(a,b):d(a,b)=2}) be symmetric, where (d) is a distance function?Which statement gives the correct definition of a symmetric relation?