Mathematics
Symmetric relation
Practice questions
On (A={1,2,3}), a supposed symmetric relation (R) contains ((1,2)) but not ((2,1)). What does this show?If (M) is the matrix of (R), what is the correct matrix condition for (R) to be symmetric?Which option shows that a symmetric relation need not be transitive?On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1),(1,3),(3,1)}). Which missing pair does not break symmetry?If a relation contains only diagonal pairs of the form ((a,a)), why will it be symmetric?On (A={1,2,3,4}), (R={(a,b):a) and (b) are both even or both odd(}). What is (R)?(R={(a,b):a^2=b^2}) is given on real numbers. Which statement about (R) is correct?For a real-life relation like (R={(a,b):a) is a friend of (b}), what is needed to consider it symmetric?On (A={1,2,3}), (R={(1,1),(1,2),(2,1),(2,2),(3,3)}). Choose the correct statement about (R).What is the best exam strategy to identify a symmetric relation?On the set (A={1,2,3}), the relation (R={(1,1),(1,2),(2,1),(2,3)}) is given. Which ordered pair must be added at minimum to make (R) symmetric?On the set (A={1,2,3,4}), the relation (R={(a,b):a+b\text{ is even}}) is defined. What type of relation is it with respect to symmetry?On (A={1,2,3,4}), let (R={(a,b):a-b\text{ is even}}). Choose the correct statement about (R).On (A={1,2,3}), the relation (R={(1,2),(2,1),(2,3),(3,2),(1,1)}) is given. Is (R) symmetric?If a relation (R) contains ((4,7)\in R) and (R) is symmetric, which pair must definitely belong to (R)?On (A={1,2,3,4}), (R={(a,b):a\leq b}) is defined. Is (R) symmetric?On (A={1,2,3,4}), (R={(a,b):|a-b|=1}). Is (R) symmetric?On (A={1,2,3,4}), (R={(a,b):a\text{ divides }b}). Choose the correct option for (R).On (A={1,2,3,4,5}), (R={(a,b):a+b=6}). Is (R) symmetric?A symmetric relation (R) on (A={1,2,3}) contains ((1,3)) and ((2,3)). Which of the following sets must definitely be a subset of (R)?