Mathematics
Symmetric relation
Practice questions
If (R) and (S) are symmetric, what is true about (R\triangle S), where (R\triangle S=(R-S)\cup(S-R))?If (R) is symmetric on a set (A), what is true about (R\cap\Delta), where (\Delta={(a,a):a\in A})?If (R) is symmetric and has no diagonal pair, which statement is correct?If (R) is symmetric and transitive and ((a,b)\in R), which pair must definitely belong to (R)?If (R) is both symmetric and antisymmetric, what is true about the off-diagonal pairs of (R)?If a relation on (A={1,2,3,4}) is both symmetric and antisymmetric, how many such relations are possible?If (R={(x,y):xy>0}) is defined on real numbers, which statement is correct about (R)?If (R={(x,y):x=2y}) is defined on real numbers, (R) is not symmetric. Which counterexample is correct?If (R) is symmetric and (R^2=R\circ R), which statement about (R^2) is correct?If (R) is symmetric, what is true about (R^3=R\circ R\circ R)?If (R=\varnothing) is a relation on any set (A), what is true about (R)?If (R=A\times A), which statement about (R) is correct?If a symmetric relation on (A={1,2,3,4,5}) has exactly (3) off-diagonal pair groups and exactly (2) diagonal pairs, how many ordered pairs are there in total?If (R={(a,b):\min(a,b)=a}) is defined on real numbers, what is true about (R)?If (R={(a,b):\max(a,b)=\max(b,a)}) is defined on real numbers, what is true about (R)?If (R={(a,b):|a-b|<5}) is defined on real numbers, what is true about (R)?If a symmetric relation on (A={1,2,3,4}) contains ((1,2),(2,1),(3,4),(4,3)) and no other off-diagonal pairs, how many off-diagonal pair groups are there?If (R) is symmetric and (R\subseteq S), which statement about (S) is correct?If (A={1,2,3}) and (R={(1,1),(2,2),(1,2),(2,1)}), which statement about (R) is correct?If a relation satisfies (R^{-1}\subseteq R), what is the correct conclusion about the symmetry of (R)?