Mathematics
Symmetric relation
Practice questions
On (A={1,2,3,4}), relation (R={(a,b):a+b=5}) is defined. Is (R) symmetric?If a relation (R) contains ((1,2),(2,1),(2,3),(3,2),(1,3)) and no other off-diagonal pair, what is necessary for symmetry?Which statement is true for a symmetric relation but generally not true for an antisymmetric relation?On (A={1,2,3,4}), how many symmetric relations must contain ((1,2)) and must not contain ((3,4))?If (A={1,2,3}) and (R={(1,1),(2,2),(1,2),(2,1),(2,3),(3,2)}), which property does (R) definitely have?If (A={1,2,3,4}) and (R={(1,1),(2,2),(3,3),(4,4),(1,3),(3,1),(2,4)}), which ordered pair must be added at minimum to make (R) symmetric?How many symmetric relations can be formed on A={1,2,3}?If (A={1,2,3}) and (R={(a,b):a+b\text{ is even}}), choose the correct statement about (R).If (A={1,2,3,4}) and (R={(a,b):a\le b}), why is (R) not symmetric?What is the number of symmetric relations on the set (A={1,2,3,4})?If the matrix of a relation is (M=\begin{bmatrix}1&0&1\0&1&0\1&0&0\end{bmatrix}), what is the correct statement about the relation?If (R) is a symmetric relation and ((5,8) \in R), which pair must definitely belong to (R)?If (A={1,2,3}) and (R={(1,2),(2,1),(2,3),(3,2)}), choose the correct statement about (R).For the relation (R={(x,y):x-y\text{ is odd}}), where (x,y\in {1,2,3,4}), which statement is correct?If (R) and (S) are two symmetric relations on (A), what is true about (R\cap S)?If (R) and (S) are two symmetric relations on (A), choose the correct statement about (R\cup S).If (A={1,2,3}) and (R={(1,1),(2,2),(3,3),(1,2),(2,1),(1,3)}), (R) is not symmetric because which pair is missing?For the relation (R={(a,b):a^2=b^2}) on the set of real numbers, what is the correct statement?On integers, the relation (R={(a,b):a-b=3}) is given. Why is it not symmetric?If (A={1,2,3,4}) and (R={(a,b):a) and (b) have the same remainder when divided by (2)(}), choose the correct statement about (R).