Mathematics
Symmetric relation
Practice questions
On (A={1,2,3}), relation (R={(1,2),(2,1),(2,3),(3,2),(1,1)}) is given. Choose the correct option.On (A={1,2,3,4}), (R={(a,b):a\le b}). Which counterexample shows that (R) is not symmetric?A relation (R) on a set (A) is symmetric. If ((4,7) \in R), what must definitely be true?If A has 5 elements, what is the number of symmetric relations on A?On (A={1,2,3}), how many symmetric relations contain ((1,2))?On A = {1, 2, 3}, how many symmetric relations do not contain (1,1)?On (A={1,2,3,4}), (R) is defined by (a \equiv b \pmod{2}). What type of relation is it?On real numbers, (R={(a,b):ab=0}). Choose the correct statement about (R).On (A={1,2,3,4}), (R={(a,b):a-b=1}). Is (R) symmetric?If (R) and (S) are symmetric relations on a set (A), what is true about (R \cap S)?If (R) and (S) are symmetric relations, which conclusion is correct about (R \cup S)?A relation (R) on a set (A) is symmetric. Choose the correct statement about (R^{-1}).Which statement gives the correct definition of a symmetric relation?Is the empty relation (\varnothing) on a non-empty set (A) symmetric or not?Why is the universal relation (A\times A) on a set (A) symmetric?On (A={1,2,3,4}), (R={(1,2),(2,1),(3,4),(4,3),(2,2)}). What is correct about (R)?On real numbers, (R={(a,b):a+b=0}). Is (R) symmetric?On (A={1,2,3,4,6}), (R={(a,b):\gcd(a,b)=2}). Choose the correct statement about (R).On (A={1,2,3,4,6}), (R={(a,b):\operatorname{lcm}(a,b)=6}). What type of relation is it?A relation (R) on a set (A) is symmetric. Which of the following need not be true?