Mathematics
Symmetric relation
Practice questions
On A = {1,2,3}, let R = {(1,1),(2,2),(3,3),(1,2),(2,1)}. Choose the correct statement.On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2)}). Why is (R) not symmetric?On a set with (5) elements, how many symmetric relations have no diagonal pair?On (A={1,2,3,4}), a symmetric relation (R) has exactly (2) diagonal pairs and exactly (2) off-diagonal mirror-pair groups. How many such relations are possible?If (R) is symmetric and ((a,b)\notin R), must ((b,a)\notin R) also be true?On (A={1,2,3}), (R={(1,2),(2,1),(2,3),(3,2)}). Choose the correct statement about (R).If the directed graph of a relation has an arrow from (x) to (y), what is necessary for the relation to be symmetric?On (A={1,2,3}), (R={(a,b):a^2=b^2}). What type of relation is (R)?On A = {1,2,3,4}, let R = {(a,b) : a + b ≤ 5}. Is R symmetric?On (A={1,2,3,4}), (R={(a,b):a\leq b}). Why is (R) not symmetric?If (R) is symmetric, which statement about (A\times A-R) is correct?On (A={1,2,3}), (R={(1,2),(2,1)}) and (S={(2,3),(3,2)}). What is correct about (R\cup S)?If (R) and (S) are symmetric, is (R-S) always symmetric?On (A={1,2,3,4}), (R={(a,b):|a-b|\text{ is even}}). What is (R)?On (A={1,2,3,4}), (R={(a,b):a-b\text{ is even}}). Choose the correct statement about (R).On (A={1,2,3,4}), (R={(a,b):a-b\text{ is odd}}). What is (R)?On a set (A), (R={(a,b):a+b=ab}). What is the correct reason for (R) being symmetric?On (A={1,2,3,4}), (R={(a,b):a+2b=6}). Is (R) symmetric?On (A={1,2,3,4}), (R={(a,b):a^2+b^2=10}). What type of relation is (R)?If (A) has (6) elements, how many symmetric relations are there on (A)?