Mathematics
Symmetric relation
Practice questions
If the matrix of a relation on (A={1,2,3}) is (M=\begin{bmatrix}1&1&0\0&1&1\0&1&1\end{bmatrix}), is the relation symmetric?If (A={1,2,3,4,5}), the number of symmetric relations on (A) equals which of the following?If R is symmetric, which statement about R⁻¹ is correct?If a relation (R) satisfies (R=R^{-1}), what is the correct conclusion about (R)?Which option gives a relation on (A={1,2,3}) that is symmetric but not reflexive?If (R) is symmetric on (A={1,2,3}) and ((1,2),(2,3),(3,1)\in R), which pairs must also be in (R) at minimum?For the relation (R={(a,b):a) divides (b)(}) on natural numbers, what is the correct statement?If (R={(a,b):|a-b|\le 2}) is defined on integers, choose the correct statement about (R).If (A={1,2,3,4}) and (R) contains exactly those pairs in which both numbers are odd or both numbers are even, which statement is correct about (R)?If (A={1,2,3}) and (R={(1,2),(2,1),(1,3),(3,1),(2,2)}), choose the correct statement about (R).If (A={1,2,3,4}) and (R={(1,2),(2,1),(1,3),(3,1),(2,4)}), what will be the smallest symmetric extension of (R)?A set (A) has (6) elements. How many relations on (A) are both symmetric and reflexive?If (A={1,2,3,4,5}), how many symmetric relations on (A) contain no diagonal pair?If (R) is symmetric and (S\subseteq R), which conclusion about (S) is always correct?If (R) and (S) are symmetric relations on (A), which statement about (R-S) is correct?If (R) and (S) are symmetric relations, which additional condition is sufficient for (R\circ S) to be symmetric?If (R={(a,b):a+b=0}) is defined on integers, what is the correct statement about (R)?If (R={(x,y):x-y>0}) is defined on real numbers, why is (R) not symmetric?If (A={1,2,3,4}) and (R={(a,b):|a-b|=2}), how many ordered pairs are in (R)?If the matrix of a relation is (M=\begin{bmatrix}0&1&1\1&1&0\1&0&1\end{bmatrix}), choose the correct statement.