Mathematics
Symmetric relation
Practice questions
Which option gives a relation that is symmetric but not reflexive, where (A={1,2,3})?Which option gives a relation that is not symmetric but contains some diagonal pairs?If the matrix of relation (R) is (\begin{pmatrix}1&0&1\0&1&0\1&0&1\end{pmatrix}), what type is (R)?If the matrix of relation (R) has (m_{23}=1) and (m_{32}=0), what can be said about (R)?If (A={1,2,3}) and (R=A\times A), why is (R) symmetric?Why is the empty relation (\varnothing) considered symmetric?On (A={1,2,3,4,5}), what type is (R={(a,b):a\equiv b \pmod{2}})?For (R={(a,b):a\equiv b \pmod{3}}) on (A={1,2,3,4,5}), which statement is correct?On (A={1,2,3,4}), why is (R={(a,b):a=b+1}) not symmetric?If (R={(a,b):a^2=b^2}) is defined on the set of integers, what type is (R)?On (A={1,2,3,4}), how many pairs are in (R={(a,b):a+b=5}), and what type is (R)?On (A={1,2,3,4}), is (R={(a,b):a-b=2}) symmetric or not?On (A={1,2,3,4}), what is the correct conclusion for (R={(a,b):|a-b|\le 1})?If (R) is symmetric and (R) contains ((2,5)) and ((4,6)), which group of pairs must be in (R)?If (R={(1,2),(2,1),(1,3),(3,1),(2,4)}), what is the minimum number of pairs needed to make it symmetric?If (R={(1,2),(2,1),(2,3),(3,2),(3,4),(4,3)}), what is (R^{-1})?In which option will (R^{-1}=R) be true?On (A={1,2,3,4}), what type is the relation (R={(a,b):\gcd(a,b)=1})?On (A={1,2,3,4,5,6}), which statement is correct for (R={(a,b):a\text{ and }b\text{ are both even}})?On (A={1,2,3,4}), why is (R={(a,b):a\text{ divides }b}) not symmetric?